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[Mental Calculation] Re: Calculating Powers, file this under "trivial entertainment"

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  • dacastro93
    I m sorry Mr. Bouman, my name is Daniel. These are nice properties! While memorizing the squares I observed that numbers that add up to 100 have their squares
    Message 1 of 24 , Dec 1, 2012
    • 0 Attachment
      I'm sorry Mr. Bouman, my name is Daniel.

      These are nice properties! While memorizing the squares I observed that numbers that add up to 100 have their squares with the same ending, for example 38 and 62. Both add up to a hundred. 38 squared is 1444 and 62 squared is 3844, so the last to digits match.

      Mnemonic is anything that can help memorizing something. It might be a word, a phrase or mental image that facilitate the process of memorizing.

      Well the squares are useful to me in multiplications, square roots and they also help to square larger numbers. The other powers I would like to memorize because I think it's fun :)

      Sorry if my english is bad. I'm from Brazil.

      Thank You

      --- In MentalCalculation@yahoogroups.com, "A.W.A.P. Bouman" <awap.bouman@...> wrote:
      >
      > Dear Mr. Dacastro93, or whom you may be,
      >
      >
      >
      > You could consider to subdivide the squares in groups with the same last
      > digits, so from 1-100 you can do 1,49,51 and 99, all their squares end on
      > 01. Then you take 2,48,52 and 98, all their squares ending on 04.
      >
      >
      >
      > What I did as a school boy during the less interesting lessons, is writing
      > all the numbers 1 up to 1.000 on a list and calculated the squares by
      > adding: 2² =1 + (2+1)=4, 3²= 4 +(2+3)=9.
      >
      >
      >
      > 670²=448900, 671²= 448900 + (670+671) = 450241.
      >
      >
      >
      > For the cubes: look after the structure. The tens increase according to- if
      > I am well informed - the iterationn of Newton.
      >
      > For 11 the increase of the tens is (3×1²×10) = 30 per ten, and indeed 11³=
      > 1331. For 21 the increase is 2×(3×1²×10) = 60, and indeed 21³ = 9261. You
      > have not everything, but there is a beginning.
      >
      >
      >
      > The following, still free of charge:
      >
      > 7³=343. IUncrease of the tens: 3×7²×10=70. Take 27³. Increase of the tens
      > 2×70= 40. So the last digits of 27³ have to end on 83. And indeed 27³=
      > 19683.
      >
      >
      >
      > As I have not the faintest idea of what mnmonics are, I cannot help you with
      > them.
      >
      >
      >
      > Did you consider what to do with the numbers you want to know by heart?
      >
      >
      >
      >
      >
      > Kindest regards,
      >
      >
      >
      >
      >
      > Willem Bouman
      >
      >
      >
      >
      >
      >
      >
      >
      >
      > Van: MentalCalculation@yahoogroups.com
      > [mailto:MentalCalculation@yahoogroups.com] Namens dacastro93
      > Verzonden: woensdag 28 november 2012 12:42
      > Aan: MentalCalculation@yahoogroups.com
      > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
      > "trivial entertainment"
      >
      >
      >
      >
      >
      > That was fun!
      >
      > The first 100 squares I memorized without the help of mnemonics. How long
      > can I go without mnemonics? I think I might try the first 100 cubes by rote
      > memorization, just like I did with the squares..
      >
      > Cheers
      >
      > --- In MentalCalculation@yahoogroups.com
      > <mailto:MentalCalculation%40yahoogroups.com> , "Jerry" <wholphin48@>
      > wrote:
      > >
      > >
      > > Here's a way to show the result of some great calculating with no work...
      > >
      > > Suppose a,b are positive integers, then you can write a^b in base a
      > precisely
      > > as a 1 followed by b zeros...
      > >
      > > For example 6^8 in base six is 100000000 That doesn't mean you have a clue
      > what that number is in base ten, the usual reference. But you have expressed
      > the result in base six precisely and instantly. However, this time I can
      > tell you that 6^8 in base ten is equal to 1,679,616 :)
      > >
      > > Good luck with the mnemonics. I just thought this trivia might give you
      > all a humorous break!!
      > >
      > > Jerry Newport Tucson, AZ
      > >
      > > --- In MentalCalculation@yahoogroups.com
      > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93" <dacastro123@>
      > wrote:
      > > >
      > > > Interesting! Like I said..I'll try to memorize the cubes of 1-100, then
      > I will come up with a mnemonic system in order to commit to memory higher
      > powers. Let's see what I can do.
      > > >
      > > > Cheers,
      > > >
      > > > Daniel
      > > >
      > > > --- In MentalCalculation@yahoogroups.com
      > <mailto:MentalCalculation%40yahoogroups.com> , "Retothejuggler"
      > <retothejuggler@> wrote:
      > > > >
      > > > > In the last months, I quit mental calculation a bit and switched over
      > to sudoku and logical puzzle solving. A few weeks ago my numbers hunger came
      > back and alongside this I found an older scientific article about Rüdiger
      > Gamm.
      > > > >
      > > > > Well, he learned the higher powers but still claims to construct
      > powers out of known powers, no idea about how.
      > > > >
      > > > > If you want to know what can be calculated, history shows:
      > > > >
      > > > > Mlle Osaka, 2 digits up to the 10.th (probably from memory), 3 digits
      > up to 8th.
      > > > >
      > > > > Oscar Verhaeghe 9 999 999 to the 5th., 40 seconds
      > > > >
      > > > > Marathe one digit up to the 20.th (probably from memory)
      > > > >
      > > > > Klein calculated a 16th.
      > > > >
      > > > > Any mnemonic armed and aarithemtic skilled person can do higher ones
      > but not in a matter of seconds.
      > > > >
      > > > > Thanks Ron again for our offline discussion.
      > > > >
      > > > >
      > > > >
      > > > > --- In MentalCalculation@yahoogroups.com
      > <mailto:MentalCalculation%40yahoogroups.com> , "rondrond1" <doerfpub@>
      > wrote:
      > > > > >
      > > > > > That's a very good question. Reto and I have discussed this offline
      > in the past, and we did not come up with a good solution for high powers. I
      > believe the number of significant digits of the logarithm would have to
      > equal the number of significant digits of the solution, although the last
      > few digits of the answer might be found from the last few digits of the
      > problem and also two of the digits can be found from 99-remainder (mod 99)
      > calculations if the rest of the digits are known. R�diger Gamm would
      > probably have memorized high powers, although I can't definitively say that
      > since I don't know the method or methods he uses.
      > > > > >
      > > > > > Ron
      > > > > >
      > > > > > --- In MentalCalculation@yahoogroups.com
      > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93" <dacastro123@>
      > wrote:
      > > > > > >
      > > > > > > Hi! I have a question for you...
      > > > > > >
      > > > > > > How can I calculate mentally high powers like, for example 41^23?
      > > > > > >
      > > > > > > I read that it can be achivied using logs, but the result will not
      > be accurate: log41 ~ 1,6128, so log 41^23 will be 37,0944. Doing 41^23 in a
      > calculator: =1,241734 x 10^37, but, with the use of antilog, I get 1,24280 x
      > 10^37. How can I find precisely every single digit of the power? How many
      > decimal places of logs will I need?
      > > > > > >
      > > > > > > And what about R�diger Gamm? Does he really have memorized the
      > powers? Does he use mnemonics?
      > > > > > >
      > > > > > > Thank You in advance
      > > > > > >
      > > > > >
      > > > >
      > > >
      > >
      >
      >
      >
      >
      >
      > [Non-text portions of this message have been removed]
      >
    • A.W.A.P. Bouman
      Dear Daniel, Well, I am a Dutchman, so neither native English speaker. But all you write, I understand. By the way: 38 and 62 end on 44, but also do 12 and
      Message 2 of 24 , Dec 2, 2012
      • 0 Attachment
        Dear Daniel,



        Well, I am a Dutchman, so neither native English speaker. But all you
        write, I understand. By the way: 38 and 62 end on 44, but also do 12 and 88.
        The difference is in the hundreds. This concerns all the squares of the even
        numbers. See eg 08 and 92, squared 64 and 8464, EH ( even Hundreds) and 42
        and 58 squared resp. 1746 and 3364 OH (Odd Hundreds).



        In the squares of the odd numbers you’ll see that the hundreds keep their
        nature. EG 13²=169, 37²=1369, 63²=3969, 87²=7569, all OH, odd hundreds.
        Later on when you study the 3 digit squares, you’ll see even thousands and
        odd thousands.

        Eg 13²=169, ET ( Even Thousand), 237²=56169 (ET), 263²=69169, 487²=237169,
        both OT, 513²=263169 and 737²=543169, both OT, 763²=582169 and
        987²=974169, both ET.

        Besides you can see 13+987=1000, 237+763=1000 etc.



        All the best with your number studies and have fun wit hit!!!!!



        I do not know how old you are. Concerning myself: at 14 I knew all the
        squares up to 1000 and shortly after that all the cubes up to 100. With that
        I can do a lot of things.





        Kindest regards,





        Willem Bouman

















        Van: MentalCalculation@yahoogroups.com
        [mailto:MentalCalculation@yahoogroups.com] Namens dacastro93
        Verzonden: zondag 2 december 2012 1:39
        Aan: MentalCalculation@yahoogroups.com
        Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
        "trivial entertainment"





        I'm sorry Mr. Bouman, my name is Daniel.

        These are nice properties! While memorizing the squares I observed that
        numbers that add up to 100 have their squares with the same ending, for
        example 38 and 62. Both add up to a hundred. 38 squared is 1444 and 62
        squared is 3844, so the last to digits match.

        Mnemonic is anything that can help memorizing something. It might be a word,
        a phrase or mental image that facilitate the process of memorizing.

        Well the squares are useful to me in multiplications, square roots and they
        also help to square larger numbers. The other powers I would like to
        memorize because I think it's fun :)

        Sorry if my english is bad. I'm from Brazil.

        Thank You

        --- In MentalCalculation@yahoogroups.com
        <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
        <awap.bouman@...> wrote:
        >
        > Dear Mr. Dacastro93, or whom you may be,
        >
        >
        >
        > You could consider to subdivide the squares in groups with the same last
        > digits, so from 1-100 you can do 1,49,51 and 99, all their squares end on
        > 01. Then you take 2,48,52 and 98, all their squares ending on 04.
        >
        >
        >
        > What I did as a school boy during the less interesting lessons, is writing
        > all the numbers 1 up to 1.000 on a list and calculated the squares by
        > adding: 2² =1 + (2+1)=4, 3²= 4 +(2+3)=9.
        >
        >
        >
        > 670²=448900, 671²= 448900 + (670+671) = 450241.
        >
        >
        >
        > For the cubes: look after the structure. The tens increase according to-
        if
        > I am well informed - the iterationn of Newton.
        >
        > For 11 the increase of the tens is (3×1²×10) = 30 per ten, and indeed 11³=
        > 1331. For 21 the increase is 2×(3×1²×10) = 60, and indeed 21³ = 9261. You
        > have not everything, but there is a beginning.
        >
        >
        >
        > The following, still free of charge:
        >
        > 7³=343. IUncrease of the tens: 3×7²×10=70. Take 27³. Increase of the tens
        > 2×70= 40. So the last digits of 27³ have to end on 83. And indeed 27³=
        > 19683.
        >
        >
        >
        > As I have not the faintest idea of what mnmonics are, I cannot help you
        with
        > them.
        >
        >
        >
        > Did you consider what to do with the numbers you want to know by heart?
        >
        >
        >
        >
        >
        > Kindest regards,
        >
        >
        >
        >
        >
        > Willem Bouman
        >
        >
        >
        >
        >
        >
        >
        >
        >
        > Van: MentalCalculation@yahoogroups.com
        <mailto:MentalCalculation%40yahoogroups.com>
        > [mailto:MentalCalculation@yahoogroups.com
        <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
        > Verzonden: woensdag 28 november 2012 12:42
        > Aan: MentalCalculation@yahoogroups.com
        <mailto:MentalCalculation%40yahoogroups.com>
        > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
        > "trivial entertainment"
        >
        >
        >
        >
        >
        > That was fun!
        >
        > The first 100 squares I memorized without the help of mnemonics. How long
        > can I go without mnemonics? I think I might try the first 100 cubes by
        rote
        > memorization, just like I did with the squares..
        >
        > Cheers
        >
        > --- In MentalCalculation@yahoogroups.com
        <mailto:MentalCalculation%40yahoogroups.com>
        > <mailto:MentalCalculation%40yahoogroups.com> , "Jerry" <wholphin48@>
        > wrote:
        > >
        > >
        > > Here's a way to show the result of some great calculating with no
        work...
        > >
        > > Suppose a,b are positive integers, then you can write a^b in base a
        > precisely
        > > as a 1 followed by b zeros...
        > >
        > > For example 6^8 in base six is 100000000 That doesn't mean you have a
        clue
        > what that number is in base ten, the usual reference. But you have
        expressed
        > the result in base six precisely and instantly. However, this time I can
        > tell you that 6^8 in base ten is equal to 1,679,616 :)
        > >
        > > Good luck with the mnemonics. I just thought this trivia might give you
        > all a humorous break!!
        > >
        > > Jerry Newport Tucson, AZ
        > >
        > > --- In MentalCalculation@yahoogroups.com
        <mailto:MentalCalculation%40yahoogroups.com>
        > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93" <dacastro123@>
        > wrote:
        > > >
        > > > Interesting! Like I said..I'll try to memorize the cubes of 1-100,
        then
        > I will come up with a mnemonic system in order to commit to memory higher
        > powers. Let's see what I can do.
        > > >
        > > > Cheers,
        > > >
        > > > Daniel
        > > >
        > > > --- In MentalCalculation@yahoogroups.com
        <mailto:MentalCalculation%40yahoogroups.com>
        > <mailto:MentalCalculation%40yahoogroups.com> , "Retothejuggler"
        > <retothejuggler@> wrote:
        > > > >
        > > > > In the last months, I quit mental calculation a bit and switched
        over
        > to sudoku and logical puzzle solving. A few weeks ago my numbers hunger
        came
        > back and alongside this I found an older scientific article about Rüdiger
        > Gamm.
        > > > >
        > > > > Well, he learned the higher powers but still claims to construct
        > powers out of known powers, no idea about how.
        > > > >
        > > > > If you want to know what can be calculated, history shows:
        > > > >
        > > > > Mlle Osaka, 2 digits up to the 10.th (probably from memory), 3
        digits
        > up to 8th.
        > > > >
        > > > > Oscar Verhaeghe 9 999 999 to the 5th., 40 seconds
        > > > >
        > > > > Marathe one digit up to the 20.th (probably from memory)
        > > > >
        > > > > Klein calculated a 16th.
        > > > >
        > > > > Any mnemonic armed and aarithemtic skilled person can do higher ones
        > but not in a matter of seconds.
        > > > >
        > > > > Thanks Ron again for our offline discussion.
        > > > >
        > > > >
        > > > >
        > > > > --- In MentalCalculation@yahoogroups.com
        <mailto:MentalCalculation%40yahoogroups.com>
        > <mailto:MentalCalculation%40yahoogroups.com> , "rondrond1" <doerfpub@>
        > wrote:
        > > > > >
        > > > > > That's a very good question. Reto and I have discussed this
        offline
        > in the past, and we did not come up with a good solution for high powers.
        I
        > believe the number of significant digits of the logarithm would have to
        > equal the number of significant digits of the solution, although the last
        > few digits of the answer might be found from the last few digits of the
        > problem and also two of the digits can be found from 99-remainder (mod 99)
        > calculations if the rest of the digits are known. R�diger Gamm would
        > probably have memorized high powers, although I can't definitively say
        that
        > since I don't know the method or methods he uses.
        > > > > >
        > > > > > Ron
        > > > > >
        > > > > > --- In MentalCalculation@yahoogroups.com
        <mailto:MentalCalculation%40yahoogroups.com>
        > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93" <dacastro123@>
        > wrote:
        > > > > > >
        > > > > > > Hi! I have a question for you...
        > > > > > >
        > > > > > > How can I calculate mentally high powers like, for example
        41^23?
        > > > > > >
        > > > > > > I read that it can be achivied using logs, but the result will
        not
        > be accurate: log41 ~ 1,6128, so log 41^23 will be 37,0944. Doing 41^23 in
        a
        > calculator: =1,241734 x 10^37, but, with the use of antilog, I get 1,24280
        x
        > 10^37. How can I find precisely every single digit of the power? How many
        > decimal places of logs will I need?
        > > > > > >
        > > > > > > And what about R�diger Gamm? Does he really have memorized the
        > powers? Does he use mnemonics?
        > > > > > >
        > > > > > > Thank You in advance
        > > > > > >
        > > > > >
        > > > >
        > > >
        > >
        >
        >
        >
        >
        >
        > [Non-text portions of this message have been removed]
        >





        [Non-text portions of this message have been removed]
      • dacastro93
        That s why I like math! There s a reason for everything, there are patterns everywhere.. I m 19 years old. Memorizing 1000 squares is very impressive! When I
        Message 3 of 24 , Dec 4, 2012
        • 0 Attachment
          That's why I like math! There's a reason for everything, there are patterns everywhere..

          I'm 19 years old. Memorizing 1000 squares is very impressive! When I was 6, I memorized the first 20 powers of 2, but that's not really impressive...

          Cheers,

          Daniel

          --- In MentalCalculation@yahoogroups.com, "A.W.A.P. Bouman" <awap.bouman@...> wrote:
          >
          > Dear Daniel,
          >
          >
          >
          > Well, I am a Dutchman, so neither native English speaker. But all you
          > write, I understand. By the way: 38 and 62 end on 44, but also do 12 and 88.
          > The difference is in the hundreds. This concerns all the squares of the even
          > numbers. See eg 08 and 92, squared 64 and 8464, EH ( even Hundreds) and 42
          > and 58 squared resp. 1746 and 3364 OH (Odd Hundreds).
          >
          >
          >
          > In the squares of the odd numbers you'll see that the hundreds keep their
          > nature. EG 13²=169, 37²=1369, 63²=3969, 87²=7569, all OH, odd hundreds.
          > Later on when you study the 3 digit squares, you'll see even thousands and
          > odd thousands.
          >
          > Eg 13²=169, ET ( Even Thousand), 237²=56169 (ET), 263²=69169, 487²=237169,
          > both OT, 513²=263169 and 737²=543169, both OT, 763²=582169 and
          > 987²=974169, both ET.
          >
          > Besides you can see 13+987=1000, 237+763=1000 etc.
          >
          >
          >
          > All the best with your number studies and have fun wit hit!!!!!
          >
          >
          >
          > I do not know how old you are. Concerning myself: at 14 I knew all the
          > squares up to 1000 and shortly after that all the cubes up to 100. With that
          > I can do a lot of things.
          >
          >
          >
          >
          >
          > Kindest regards,
          >
          >
          >
          >
          >
          > Willem Bouman
          >
          >
          >
          >
          >
          >
          >
          >
          >
          >
          >
          >
          >
          >
          >
          >
          >
          > Van: MentalCalculation@yahoogroups.com
          > [mailto:MentalCalculation@yahoogroups.com] Namens dacastro93
          > Verzonden: zondag 2 december 2012 1:39
          > Aan: MentalCalculation@yahoogroups.com
          > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
          > "trivial entertainment"
          >
          >
          >
          >
          >
          > I'm sorry Mr. Bouman, my name is Daniel.
          >
          > These are nice properties! While memorizing the squares I observed that
          > numbers that add up to 100 have their squares with the same ending, for
          > example 38 and 62. Both add up to a hundred. 38 squared is 1444 and 62
          > squared is 3844, so the last to digits match.
          >
          > Mnemonic is anything that can help memorizing something. It might be a word,
          > a phrase or mental image that facilitate the process of memorizing.
          >
          > Well the squares are useful to me in multiplications, square roots and they
          > also help to square larger numbers. The other powers I would like to
          > memorize because I think it's fun :)
          >
          > Sorry if my english is bad. I'm from Brazil.
          >
          > Thank You
          >
          > --- In MentalCalculation@yahoogroups.com
          > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
          > <awap.bouman@> wrote:
          > >
          > > Dear Mr. Dacastro93, or whom you may be,
          > >
          > >
          > >
          > > You could consider to subdivide the squares in groups with the same last
          > > digits, so from 1-100 you can do 1,49,51 and 99, all their squares end on
          > > 01. Then you take 2,48,52 and 98, all their squares ending on 04.
          > >
          > >
          > >
          > > What I did as a school boy during the less interesting lessons, is writing
          > > all the numbers 1 up to 1.000 on a list and calculated the squares by
          > > adding: 2² =1 + (2+1)=4, 3²= 4 +(2+3)=9.
          > >
          > >
          > >
          > > 670²=448900, 671²= 448900 + (670+671) = 450241.
          > >
          > >
          > >
          > > For the cubes: look after the structure. The tens increase according to-
          > if
          > > I am well informed - the iterationn of Newton.
          > >
          > > For 11 the increase of the tens is (3×1²×10) = 30 per ten, and indeed 11³=
          > > 1331. For 21 the increase is 2×(3×1²×10) = 60, and indeed 21³ = 9261. You
          > > have not everything, but there is a beginning.
          > >
          > >
          > >
          > > The following, still free of charge:
          > >
          > > 7³=343. IUncrease of the tens: 3×7²×10=70. Take 27³. Increase of the tens
          > > 2×70= 40. So the last digits of 27³ have to end on 83. And indeed 27³=
          > > 19683.
          > >
          > >
          > >
          > > As I have not the faintest idea of what mnmonics are, I cannot help you
          > with
          > > them.
          > >
          > >
          > >
          > > Did you consider what to do with the numbers you want to know by heart?
          > >
          > >
          > >
          > >
          > >
          > > Kindest regards,
          > >
          > >
          > >
          > >
          > >
          > > Willem Bouman
          > >
          > >
          > >
          > >
          > >
          > >
          > >
          > >
          > >
          > > Van: MentalCalculation@yahoogroups.com
          > <mailto:MentalCalculation%40yahoogroups.com>
          > > [mailto:MentalCalculation@yahoogroups.com
          > <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
          > > Verzonden: woensdag 28 november 2012 12:42
          > > Aan: MentalCalculation@yahoogroups.com
          > <mailto:MentalCalculation%40yahoogroups.com>
          > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
          > > "trivial entertainment"
          > >
          > >
          > >
          > >
          > >
          > > That was fun!
          > >
          > > The first 100 squares I memorized without the help of mnemonics. How long
          > > can I go without mnemonics? I think I might try the first 100 cubes by
          > rote
          > > memorization, just like I did with the squares..
          > >
          > > Cheers
          > >
          > > --- In MentalCalculation@yahoogroups.com
          > <mailto:MentalCalculation%40yahoogroups.com>
          > > <mailto:MentalCalculation%40yahoogroups.com> , "Jerry" <wholphin48@>
          > > wrote:
          > > >
          > > >
          > > > Here's a way to show the result of some great calculating with no
          > work...
          > > >
          > > > Suppose a,b are positive integers, then you can write a^b in base a
          > > precisely
          > > > as a 1 followed by b zeros...
          > > >
          > > > For example 6^8 in base six is 100000000 That doesn't mean you have a
          > clue
          > > what that number is in base ten, the usual reference. But you have
          > expressed
          > > the result in base six precisely and instantly. However, this time I can
          > > tell you that 6^8 in base ten is equal to 1,679,616 :)
          > > >
          > > > Good luck with the mnemonics. I just thought this trivia might give you
          > > all a humorous break!!
          > > >
          > > > Jerry Newport Tucson, AZ
          > > >
          > > > --- In MentalCalculation@yahoogroups.com
          > <mailto:MentalCalculation%40yahoogroups.com>
          > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93" <dacastro123@>
          > > wrote:
          > > > >
          > > > > Interesting! Like I said..I'll try to memorize the cubes of 1-100,
          > then
          > > I will come up with a mnemonic system in order to commit to memory higher
          > > powers. Let's see what I can do.
          > > > >
          > > > > Cheers,
          > > > >
          > > > > Daniel
          > > > >
          > > > > --- In MentalCalculation@yahoogroups.com
          > <mailto:MentalCalculation%40yahoogroups.com>
          > > <mailto:MentalCalculation%40yahoogroups.com> , "Retothejuggler"
          > > <retothejuggler@> wrote:
          > > > > >
          > > > > > In the last months, I quit mental calculation a bit and switched
          > over
          > > to sudoku and logical puzzle solving. A few weeks ago my numbers hunger
          > came
          > > back and alongside this I found an older scientific article about Rüdiger
          > > Gamm.
          > > > > >
          > > > > > Well, he learned the higher powers but still claims to construct
          > > powers out of known powers, no idea about how.
          > > > > >
          > > > > > If you want to know what can be calculated, history shows:
          > > > > >
          > > > > > Mlle Osaka, 2 digits up to the 10.th (probably from memory), 3
          > digits
          > > up to 8th.
          > > > > >
          > > > > > Oscar Verhaeghe 9 999 999 to the 5th., 40 seconds
          > > > > >
          > > > > > Marathe one digit up to the 20.th (probably from memory)
          > > > > >
          > > > > > Klein calculated a 16th.
          > > > > >
          > > > > > Any mnemonic armed and aarithemtic skilled person can do higher ones
          > > but not in a matter of seconds.
          > > > > >
          > > > > > Thanks Ron again for our offline discussion.
          > > > > >
          > > > > >
          > > > > >
          > > > > > --- In MentalCalculation@yahoogroups.com
          > <mailto:MentalCalculation%40yahoogroups.com>
          > > <mailto:MentalCalculation%40yahoogroups.com> , "rondrond1" <doerfpub@>
          > > wrote:
          > > > > > >
          > > > > > > That's a very good question. Reto and I have discussed this
          > offline
          > > in the past, and we did not come up with a good solution for high powers.
          > I
          > > believe the number of significant digits of the logarithm would have to
          > > equal the number of significant digits of the solution, although the last
          > > few digits of the answer might be found from the last few digits of the
          > > problem and also two of the digits can be found from 99-remainder (mod 99)
          > > calculations if the rest of the digits are known. R�diger Gamm would
          > > probably have memorized high powers, although I can't definitively say
          > that
          > > since I don't know the method or methods he uses.
          > > > > > >
          > > > > > > Ron
          > > > > > >
          > > > > > > --- In MentalCalculation@yahoogroups.com
          > <mailto:MentalCalculation%40yahoogroups.com>
          > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93" <dacastro123@>
          > > wrote:
          > > > > > > >
          > > > > > > > Hi! I have a question for you...
          > > > > > > >
          > > > > > > > How can I calculate mentally high powers like, for example
          > 41^23?
          > > > > > > >
          > > > > > > > I read that it can be achivied using logs, but the result will
          > not
          > > be accurate: log41 ~ 1,6128, so log 41^23 will be 37,0944. Doing 41^23 in
          > a
          > > calculator: =1,241734 x 10^37, but, with the use of antilog, I get 1,24280
          > x
          > > 10^37. How can I find precisely every single digit of the power? How many
          > > decimal places of logs will I need?
          > > > > > > >
          > > > > > > > And what about R�diger Gamm? Does he really have memorized the
          > > powers? Does he use mnemonics?
          > > > > > > >
          > > > > > > > Thank You in advance
          > > > > > > >
          > > > > > >
          > > > > >
          > > > >
          > > >
          > >
          > >
          > >
          > >
          > >
          > > [Non-text portions of this message have been removed]
          > >
          >
          >
          >
          >
          >
          > [Non-text portions of this message have been removed]
          >
        • Retothejuggler
          I`m wondering what other numbers friends here have stored in their minds, my lame work is just 2-digit squares, 20 decimals of Pi, cubes up to 30 and fith up
          Message 4 of 24 , Dec 5, 2012
          • 0 Attachment
            I`m wondering what other numbers friends here have stored in their minds, my lame work is just 2-digit squares, 20 decimals of Pi, cubes up to 30 and fith up to 12 right now and some primes...

            But I`m just back in it...there is hope...


            --- In MentalCalculation@yahoogroups.com, "dacastro93" <dacastro123@...> wrote:
            >
            > That's why I like math! There's a reason for everything, there are patterns everywhere..
            >
            > I'm 19 years old. Memorizing 1000 squares is very impressive! When I was 6, I memorized the first 20 powers of 2, but that's not really impressive...
            >
            > Cheers,
            >
            > Daniel
            >
            > --- In MentalCalculation@yahoogroups.com, "A.W.A.P. Bouman" <awap.bouman@> wrote:
            > >
            > > Dear Daniel,
            > >
            > >
            > >
            > > Well, I am a Dutchman, so neither native English speaker. But all you
            > > write, I understand. By the way: 38 and 62 end on 44, but also do 12 and 88.
            > > The difference is in the hundreds. This concerns all the squares of the even
            > > numbers. See eg 08 and 92, squared 64 and 8464, EH ( even Hundreds) and 42
            > > and 58 squared resp. 1746 and 3364 OH (Odd Hundreds).
            > >
            > >
            > >
            > > In the squares of the odd numbers you'll see that the hundreds keep their
            > > nature. EG 13²=169, 37²=1369, 63²=3969, 87²=7569, all OH, odd hundreds.
            > > Later on when you study the 3 digit squares, you'll see even thousands and
            > > odd thousands.
            > >
            > > Eg 13²=169, ET ( Even Thousand), 237²=56169 (ET), 263²=69169, 487²=237169,
            > > both OT, 513²=263169 and 737²=543169, both OT, 763²=582169 and
            > > 987²=974169, both ET.
            > >
            > > Besides you can see 13+987=1000, 237+763=1000 etc.
            > >
            > >
            > >
            > > All the best with your number studies and have fun wit hit!!!!!
            > >
            > >
            > >
            > > I do not know how old you are. Concerning myself: at 14 I knew all the
            > > squares up to 1000 and shortly after that all the cubes up to 100. With that
            > > I can do a lot of things.
            > >
            > >
            > >
            > >
            > >
            > > Kindest regards,
            > >
            > >
            > >
            > >
            > >
            > > Willem Bouman
            > >
            > >
            > >
            > >
            > >
            > >
            > >
            > >
            > >
            > >
            > >
            > >
            > >
            > >
            > >
            > >
            > >
            > > Van: MentalCalculation@yahoogroups.com
            > > [mailto:MentalCalculation@yahoogroups.com] Namens dacastro93
            > > Verzonden: zondag 2 december 2012 1:39
            > > Aan: MentalCalculation@yahoogroups.com
            > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
            > > "trivial entertainment"
            > >
            > >
            > >
            > >
            > >
            > > I'm sorry Mr. Bouman, my name is Daniel.
            > >
            > > These are nice properties! While memorizing the squares I observed that
            > > numbers that add up to 100 have their squares with the same ending, for
            > > example 38 and 62. Both add up to a hundred. 38 squared is 1444 and 62
            > > squared is 3844, so the last to digits match.
            > >
            > > Mnemonic is anything that can help memorizing something. It might be a word,
            > > a phrase or mental image that facilitate the process of memorizing.
            > >
            > > Well the squares are useful to me in multiplications, square roots and they
            > > also help to square larger numbers. The other powers I would like to
            > > memorize because I think it's fun :)
            > >
            > > Sorry if my english is bad. I'm from Brazil.
            > >
            > > Thank You
            > >
            > > --- In MentalCalculation@yahoogroups.com
            > > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
            > > <awap.bouman@> wrote:
            > > >
            > > > Dear Mr. Dacastro93, or whom you may be,
            > > >
            > > >
            > > >
            > > > You could consider to subdivide the squares in groups with the same last
            > > > digits, so from 1-100 you can do 1,49,51 and 99, all their squares end on
            > > > 01. Then you take 2,48,52 and 98, all their squares ending on 04.
            > > >
            > > >
            > > >
            > > > What I did as a school boy during the less interesting lessons, is writing
            > > > all the numbers 1 up to 1.000 on a list and calculated the squares by
            > > > adding: 2² =1 + (2+1)=4, 3²= 4 +(2+3)=9.
            > > >
            > > >
            > > >
            > > > 670²=448900, 671²= 448900 + (670+671) = 450241.
            > > >
            > > >
            > > >
            > > > For the cubes: look after the structure. The tens increase according to-
            > > if
            > > > I am well informed - the iterationn of Newton.
            > > >
            > > > For 11 the increase of the tens is (3×1²×10) = 30 per ten, and indeed 11³=
            > > > 1331. For 21 the increase is 2×(3×1²×10) = 60, and indeed 21³ = 9261. You
            > > > have not everything, but there is a beginning.
            > > >
            > > >
            > > >
            > > > The following, still free of charge:
            > > >
            > > > 7³=343. IUncrease of the tens: 3×7²×10=70. Take 27³. Increase of the tens
            > > > 2×70= 40. So the last digits of 27³ have to end on 83. And indeed 27³=
            > > > 19683.
            > > >
            > > >
            > > >
            > > > As I have not the faintest idea of what mnmonics are, I cannot help you
            > > with
            > > > them.
            > > >
            > > >
            > > >
            > > > Did you consider what to do with the numbers you want to know by heart?
            > > >
            > > >
            > > >
            > > >
            > > >
            > > > Kindest regards,
            > > >
            > > >
            > > >
            > > >
            > > >
            > > > Willem Bouman
            > > >
            > > >
            > > >
            > > >
            > > >
            > > >
            > > >
            > > >
            > > >
            > > > Van: MentalCalculation@yahoogroups.com
            > > <mailto:MentalCalculation%40yahoogroups.com>
            > > > [mailto:MentalCalculation@yahoogroups.com
            > > <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
            > > > Verzonden: woensdag 28 november 2012 12:42
            > > > Aan: MentalCalculation@yahoogroups.com
            > > <mailto:MentalCalculation%40yahoogroups.com>
            > > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
            > > > "trivial entertainment"
            > > >
            > > >
            > > >
            > > >
            > > >
            > > > That was fun!
            > > >
            > > > The first 100 squares I memorized without the help of mnemonics. How long
            > > > can I go without mnemonics? I think I might try the first 100 cubes by
            > > rote
            > > > memorization, just like I did with the squares..
            > > >
            > > > Cheers
            > > >
            > > > --- In MentalCalculation@yahoogroups.com
            > > <mailto:MentalCalculation%40yahoogroups.com>
            > > > <mailto:MentalCalculation%40yahoogroups.com> , "Jerry" <wholphin48@>
            > > > wrote:
            > > > >
            > > > >
            > > > > Here's a way to show the result of some great calculating with no
            > > work...
            > > > >
            > > > > Suppose a,b are positive integers, then you can write a^b in base a
            > > > precisely
            > > > > as a 1 followed by b zeros...
            > > > >
            > > > > For example 6^8 in base six is 100000000 That doesn't mean you have a
            > > clue
            > > > what that number is in base ten, the usual reference. But you have
            > > expressed
            > > > the result in base six precisely and instantly. However, this time I can
            > > > tell you that 6^8 in base ten is equal to 1,679,616 :)
            > > > >
            > > > > Good luck with the mnemonics. I just thought this trivia might give you
            > > > all a humorous break!!
            > > > >
            > > > > Jerry Newport Tucson, AZ
            > > > >
            > > > > --- In MentalCalculation@yahoogroups.com
            > > <mailto:MentalCalculation%40yahoogroups.com>
            > > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93" <dacastro123@>
            > > > wrote:
            > > > > >
            > > > > > Interesting! Like I said..I'll try to memorize the cubes of 1-100,
            > > then
            > > > I will come up with a mnemonic system in order to commit to memory higher
            > > > powers. Let's see what I can do.
            > > > > >
            > > > > > Cheers,
            > > > > >
            > > > > > Daniel
            > > > > >
            > > > > > --- In MentalCalculation@yahoogroups.com
            > > <mailto:MentalCalculation%40yahoogroups.com>
            > > > <mailto:MentalCalculation%40yahoogroups.com> , "Retothejuggler"
            > > > <retothejuggler@> wrote:
            > > > > > >
            > > > > > > In the last months, I quit mental calculation a bit and switched
            > > over
            > > > to sudoku and logical puzzle solving. A few weeks ago my numbers hunger
            > > came
            > > > back and alongside this I found an older scientific article about Rüdiger
            > > > Gamm.
            > > > > > >
            > > > > > > Well, he learned the higher powers but still claims to construct
            > > > powers out of known powers, no idea about how.
            > > > > > >
            > > > > > > If you want to know what can be calculated, history shows:
            > > > > > >
            > > > > > > Mlle Osaka, 2 digits up to the 10.th (probably from memory), 3
            > > digits
            > > > up to 8th.
            > > > > > >
            > > > > > > Oscar Verhaeghe 9 999 999 to the 5th., 40 seconds
            > > > > > >
            > > > > > > Marathe one digit up to the 20.th (probably from memory)
            > > > > > >
            > > > > > > Klein calculated a 16th.
            > > > > > >
            > > > > > > Any mnemonic armed and aarithemtic skilled person can do higher ones
            > > > but not in a matter of seconds.
            > > > > > >
            > > > > > > Thanks Ron again for our offline discussion.
            > > > > > >
            > > > > > >
            > > > > > >
            > > > > > > --- In MentalCalculation@yahoogroups.com
            > > <mailto:MentalCalculation%40yahoogroups.com>
            > > > <mailto:MentalCalculation%40yahoogroups.com> , "rondrond1" <doerfpub@>
            > > > wrote:
            > > > > > > >
            > > > > > > > That's a very good question. Reto and I have discussed this
            > > offline
            > > > in the past, and we did not come up with a good solution for high powers.
            > > I
            > > > believe the number of significant digits of the logarithm would have to
            > > > equal the number of significant digits of the solution, although the last
            > > > few digits of the answer might be found from the last few digits of the
            > > > problem and also two of the digits can be found from 99-remainder (mod 99)
            > > > calculations if the rest of the digits are known. R�diger Gamm would
            > > > probably have memorized high powers, although I can't definitively say
            > > that
            > > > since I don't know the method or methods he uses.
            > > > > > > >
            > > > > > > > Ron
            > > > > > > >
            > > > > > > > --- In MentalCalculation@yahoogroups.com
            > > <mailto:MentalCalculation%40yahoogroups.com>
            > > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93" <dacastro123@>
            > > > wrote:
            > > > > > > > >
            > > > > > > > > Hi! I have a question for you...
            > > > > > > > >
            > > > > > > > > How can I calculate mentally high powers like, for example
            > > 41^23?
            > > > > > > > >
            > > > > > > > > I read that it can be achivied using logs, but the result will
            > > not
            > > > be accurate: log41 ~ 1,6128, so log 41^23 will be 37,0944. Doing 41^23 in
            > > a
            > > > calculator: =1,241734 x 10^37, but, with the use of antilog, I get 1,24280
            > > x
            > > > 10^37. How can I find precisely every single digit of the power? How many
            > > > decimal places of logs will I need?
            > > > > > > > >
            > > > > > > > > And what about R�diger Gamm? Does he really have memorized the
            > > > powers? Does he use mnemonics?
            > > > > > > > >
            > > > > > > > > Thank You in advance
            > > > > > > > >
            > > > > > > >
            > > > > > >
            > > > > >
            > > > >
            > > >
            > > >
            > > >
            > > >
            > > >
            > > > [Non-text portions of this message have been removed]
            > > >
            > >
            > >
            > >
            > >
            > >
            > > [Non-text portions of this message have been removed]
            > >
            >
          • A.W.A.P. Bouman
            Dear fellow calculators, What should be in someones memory? At the moment I was aware of my talent memorising the squares up to 1.000 went more or less
            Message 5 of 24 , Dec 5, 2012
            • 0 Attachment
              Dear fellow calculators,



              What should be in someones memory? At the moment I was aware of my talent
              memorising the squares up to 1.000 went more or less automatically. I
              started with 1 and by addibng I came up to 1.000. My memory must be a
              very good one: they are still there.

              In the same way the cubes up to 100.

              All the multiplications of 2 digit numbers were there from about my 9th
              year.



              This is not very impressive, but with good algoritms one can do a lot more.



              I am not perfect in it, but can do – owing to the cross method which taught
              me Wim Klein – multiplications of 8 digit numbers.



              Jan van Koningsveld and Robert Fountain taught me decimal roots, and owing
              tot hat knowledge I can do them , besides integer roots up to about 18
              digits.

              Andy Robertshaw told interesting things about decimal cube roots.



              Having found the structure in the cubes I created an algortim and so can do
              integer cube roots up to 24 digits.



              I have no idea what to do with x-decimals of pi.

              Last year I learnt the logaritms up to 100. They are gone because of
              neglecting. But surely they are helpful in decimal roots, especially the
              deep ones.



              For the younger ones amongst us I give the advise: consider which
              possibilities there are in what you intend to do and then decide what you
              want to memorise.



              Memorising “blindly” a lot of numbers is not very creative, so think very
              well before beginning “a hell of a job”.







              Kindest regards,





              Willem Bouman



























              Van: MentalCalculation@yahoogroups.com
              [mailto:MentalCalculation@yahoogroups.com] Namens Retothejuggler
              Verzonden: woensdag 5 december 2012 12:13
              Aan: MentalCalculation@yahoogroups.com
              Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
              "trivial entertainment"





              I`m wondering what other numbers friends here have stored in their minds, my
              lame work is just 2-digit squares, 20 decimals of Pi, cubes up to 30 and
              fith up to 12 right now and some primes...

              But I`m just back in it...there is hope...

              --- In MentalCalculation@yahoogroups.com
              <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
              <dacastro123@...> wrote:
              >
              > That's why I like math! There's a reason for everything, there are
              patterns everywhere..
              >
              > I'm 19 years old. Memorizing 1000 squares is very impressive! When I was
              6, I memorized the first 20 powers of 2, but that's not really impressive...
              >
              > Cheers,
              >
              > Daniel
              >
              > --- In MentalCalculation@yahoogroups.com
              <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
              <awap.bouman@> wrote:
              > >
              > > Dear Daniel,
              > >
              > >
              > >
              > > Well, I am a Dutchman, so neither native English speaker. But all you
              > > write, I understand. By the way: 38 and 62 end on 44, but also do 12 and
              88.
              > > The difference is in the hundreds. This concerns all the squares of the
              even
              > > numbers. See eg 08 and 92, squared 64 and 8464, EH ( even Hundreds) and
              42
              > > and 58 squared resp. 1746 and 3364 OH (Odd Hundreds).
              > >
              > >
              > >
              > > In the squares of the odd numbers you'll see that the hundreds keep
              their
              > > nature. EG 13²=169, 37²=1369, 63²=3969, 87²=7569, all OH, odd hundreds.
              > > Later on when you study the 3 digit squares, you'll see even thousands
              and
              > > odd thousands.
              > >
              > > Eg 13²=169, ET ( Even Thousand), 237²=56169 (ET), 263²=69169,
              487²=237169,
              > > both OT, 513²=263169 and 737²=543169, both OT, 763²=582169 and
              > > 987²=974169, both ET.
              > >
              > > Besides you can see 13+987=1000, 237+763=1000 etc.
              > >
              > >
              > >
              > > All the best with your number studies and have fun wit hit!!!!!
              > >
              > >
              > >
              > > I do not know how old you are. Concerning myself: at 14 I knew all the
              > > squares up to 1000 and shortly after that all the cubes up to 100. With
              that
              > > I can do a lot of things.
              > >
              > >
              > >
              > >
              > >
              > > Kindest regards,
              > >
              > >
              > >
              > >
              > >
              > > Willem Bouman
              > >
              > >
              > >
              > >
              > >
              > >
              > >
              > >
              > >
              > >
              > >
              > >
              > >
              > >
              > >
              > >
              > >
              > > Van: MentalCalculation@yahoogroups.com
              <mailto:MentalCalculation%40yahoogroups.com>
              > > [mailto:MentalCalculation@yahoogroups.com
              <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
              > > Verzonden: zondag 2 december 2012 1:39
              > > Aan: MentalCalculation@yahoogroups.com
              <mailto:MentalCalculation%40yahoogroups.com>
              > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
              > > "trivial entertainment"
              > >
              > >
              > >
              > >
              > >
              > > I'm sorry Mr. Bouman, my name is Daniel.
              > >
              > > These are nice properties! While memorizing the squares I observed that
              > > numbers that add up to 100 have their squares with the same ending, for
              > > example 38 and 62. Both add up to a hundred. 38 squared is 1444 and 62
              > > squared is 3844, so the last to digits match.
              > >
              > > Mnemonic is anything that can help memorizing something. It might be a
              word,
              > > a phrase or mental image that facilitate the process of memorizing.
              > >
              > > Well the squares are useful to me in multiplications, square roots and
              they
              > > also help to square larger numbers. The other powers I would like to
              > > memorize because I think it's fun :)
              > >
              > > Sorry if my english is bad. I'm from Brazil.
              > >
              > > Thank You
              > >
              > > --- In MentalCalculation@yahoogroups.com
              <mailto:MentalCalculation%40yahoogroups.com>
              > > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
              > > <awap.bouman@> wrote:
              > > >
              > > > Dear Mr. Dacastro93, or whom you may be,
              > > >
              > > >
              > > >
              > > > You could consider to subdivide the squares in groups with the same
              last
              > > > digits, so from 1-100 you can do 1,49,51 and 99, all their squares end
              on
              > > > 01. Then you take 2,48,52 and 98, all their squares ending on 04.
              > > >
              > > >
              > > >
              > > > What I did as a school boy during the less interesting lessons, is
              writing
              > > > all the numbers 1 up to 1.000 on a list and calculated the squares by
              > > > adding: 2² =1 + (2+1)=4, 3²= 4 +(2+3)=9.
              > > >
              > > >
              > > >
              > > > 670²=448900, 671²= 448900 + (670+671) = 450241.
              > > >
              > > >
              > > >
              > > > For the cubes: look after the structure. The tens increase according
              to-
              > > if
              > > > I am well informed - the iterationn of Newton.
              > > >
              > > > For 11 the increase of the tens is (3×1²×10) = 30 per ten, and indeed
              11³=
              > > > 1331. For 21 the increase is 2×(3×1²×10) = 60, and indeed 21³ = 9261.
              You
              > > > have not everything, but there is a beginning.
              > > >
              > > >
              > > >
              > > > The following, still free of charge:
              > > >
              > > > 7³=343. IUncrease of the tens: 3×7²×10=70. Take 27³. Increase of the
              tens
              > > > 2×70= 40. So the last digits of 27³ have to end on 83. And indeed 27³=
              > > > 19683.
              > > >
              > > >
              > > >
              > > > As I have not the faintest idea of what mnmonics are, I cannot help
              you
              > > with
              > > > them.
              > > >
              > > >
              > > >
              > > > Did you consider what to do with the numbers you want to know by
              heart?
              > > >
              > > >
              > > >
              > > >
              > > >
              > > > Kindest regards,
              > > >
              > > >
              > > >
              > > >
              > > >
              > > > Willem Bouman
              > > >
              > > >
              > > >
              > > >
              > > >
              > > >
              > > >
              > > >
              > > >
              > > > Van: MentalCalculation@yahoogroups.com
              <mailto:MentalCalculation%40yahoogroups.com>
              > > <mailto:MentalCalculation%40yahoogroups.com>
              > > > [mailto:MentalCalculation@yahoogroups.com
              <mailto:MentalCalculation%40yahoogroups.com>
              > > <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
              > > > Verzonden: woensdag 28 november 2012 12:42
              > > > Aan: MentalCalculation@yahoogroups.com
              <mailto:MentalCalculation%40yahoogroups.com>
              > > <mailto:MentalCalculation%40yahoogroups.com>
              > > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this
              under
              > > > "trivial entertainment"
              > > >
              > > >
              > > >
              > > >
              > > >
              > > > That was fun!
              > > >
              > > > The first 100 squares I memorized without the help of mnemonics. How
              long
              > > > can I go without mnemonics? I think I might try the first 100 cubes by
              > > rote
              > > > memorization, just like I did with the squares..
              > > >
              > > > Cheers
              > > >
              > > > --- In MentalCalculation@yahoogroups.com
              <mailto:MentalCalculation%40yahoogroups.com>
              > > <mailto:MentalCalculation%40yahoogroups.com>
              > > > <mailto:MentalCalculation%40yahoogroups.com> , "Jerry" <wholphin48@>
              > > > wrote:
              > > > >
              > > > >
              > > > > Here's a way to show the result of some great calculating with no
              > > work...
              > > > >
              > > > > Suppose a,b are positive integers, then you can write a^b in base a
              > > > precisely
              > > > > as a 1 followed by b zeros...
              > > > >
              > > > > For example 6^8 in base six is 100000000 That doesn't mean you have
              a
              > > clue
              > > > what that number is in base ten, the usual reference. But you have
              > > expressed
              > > > the result in base six precisely and instantly. However, this time I
              can
              > > > tell you that 6^8 in base ten is equal to 1,679,616 :)
              > > > >
              > > > > Good luck with the mnemonics. I just thought this trivia might give
              you
              > > > all a humorous break!!
              > > > >
              > > > > Jerry Newport Tucson, AZ
              > > > >
              > > > > --- In MentalCalculation@yahoogroups.com
              <mailto:MentalCalculation%40yahoogroups.com>
              > > <mailto:MentalCalculation%40yahoogroups.com>
              > > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
              <dacastro123@>
              > > > wrote:
              > > > > >
              > > > > > Interesting! Like I said..I'll try to memorize the cubes of 1-100,
              > > then
              > > > I will come up with a mnemonic system in order to commit to memory
              higher
              > > > powers. Let's see what I can do.
              > > > > >
              > > > > > Cheers,
              > > > > >
              > > > > > Daniel
              > > > > >
              > > > > > --- In MentalCalculation@yahoogroups.com
              <mailto:MentalCalculation%40yahoogroups.com>
              > > <mailto:MentalCalculation%40yahoogroups.com>
              > > > <mailto:MentalCalculation%40yahoogroups.com> , "Retothejuggler"
              > > > <retothejuggler@> wrote:
              > > > > > >
              > > > > > > In the last months, I quit mental calculation a bit and switched
              > > over
              > > > to sudoku and logical puzzle solving. A few weeks ago my numbers
              hunger
              > > came
              > > > back and alongside this I found an older scientific article about
              Rüdiger
              > > > Gamm.
              > > > > > >
              > > > > > > Well, he learned the higher powers but still claims to construct
              > > > powers out of known powers, no idea about how.
              > > > > > >
              > > > > > > If you want to know what can be calculated, history shows:
              > > > > > >
              > > > > > > Mlle Osaka, 2 digits up to the 10.th (probably from memory), 3
              > > digits
              > > > up to 8th.
              > > > > > >
              > > > > > > Oscar Verhaeghe 9 999 999 to the 5th., 40 seconds
              > > > > > >
              > > > > > > Marathe one digit up to the 20.th (probably from memory)
              > > > > > >
              > > > > > > Klein calculated a 16th.
              > > > > > >
              > > > > > > Any mnemonic armed and aarithemtic skilled person can do higher
              ones
              > > > but not in a matter of seconds.
              > > > > > >
              > > > > > > Thanks Ron again for our offline discussion.
              > > > > > >
              > > > > > >
              > > > > > >
              > > > > > > --- In MentalCalculation@yahoogroups.com
              <mailto:MentalCalculation%40yahoogroups.com>
              > > <mailto:MentalCalculation%40yahoogroups.com>
              > > > <mailto:MentalCalculation%40yahoogroups.com> , "rondrond1" <doerfpub@>
              > > > wrote:
              > > > > > > >
              > > > > > > > That's a very good question. Reto and I have discussed this
              > > offline
              > > > in the past, and we did not come up with a good solution for high
              powers.
              > > I
              > > > believe the number of significant digits of the logarithm would have
              to
              > > > equal the number of significant digits of the solution, although the
              last
              > > > few digits of the answer might be found from the last few digits of
              the
              > > > problem and also two of the digits can be found from 99-remainder (mod
              99)
              > > > calculations if the rest of the digits are known. R�diger Gamm would
              > > > probably have memorized high powers, although I can't definitively say
              > > that
              > > > since I don't know the method or methods he uses.
              > > > > > > >
              > > > > > > > Ron
              > > > > > > >
              > > > > > > > --- In MentalCalculation@yahoogroups.com
              <mailto:MentalCalculation%40yahoogroups.com>
              > > <mailto:MentalCalculation%40yahoogroups.com>
              > > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
              <dacastro123@>
              > > > wrote:
              > > > > > > > >
              > > > > > > > > Hi! I have a question for you...
              > > > > > > > >
              > > > > > > > > How can I calculate mentally high powers like, for example
              > > 41^23?
              > > > > > > > >
              > > > > > > > > I read that it can be achivied using logs, but the result
              will
              > > not
              > > > be accurate: log41 ~ 1,6128, so log 41^23 will be 37,0944. Doing 41^23
              in
              > > a
              > > > calculator: =1,241734 x 10^37, but, with the use of antilog, I get
              1,24280
              > > x
              > > > 10^37. How can I find precisely every single digit of the power? How
              many
              > > > decimal places of logs will I need?
              > > > > > > > >
              > > > > > > > > And what about R�diger Gamm? Does he really have memorized
              the
              > > > powers? Does he use mnemonics?
              > > > > > > > >
              > > > > > > > > Thank You in advance
              > > > > > > > >
              > > > > > > >
              > > > > > >
              > > > > >
              > > > >
              > > >
              > > >
              > > >
              > > >
              > > >
              > > > [Non-text portions of this message have been removed]
              > > >
              > >
              > >
              > >
              > >
              > >
              > > [Non-text portions of this message have been removed]
              > >
              >





              [Non-text portions of this message have been removed]
            • Retothejuggler
              Dear Willem How have you calculated the cubes? They can`t be broken down simply in a row of additions (which you used to learn squares). It would be
              Message 6 of 24 , Dec 6, 2012
              • 0 Attachment
                Dear Willem

                How have you calculated the cubes? They can`t be broken down simply in a row of additions (which you used to learn squares).

                It would be interesting to see your skills in memorizing numbers without mnemotechnic pictures.

                You`re doing this for years and are miles away from most, but I`ll choose my numbers carefully :-).

                Pi is just for fun.

                Thanks for your input.

                Greetings Reto

                --- In MentalCalculation@yahoogroups.com, "A.W.A.P. Bouman" <awap.bouman@...> wrote:
                >
                > Dear fellow calculators,
                >
                >
                >
                > What should be in someones memory? At the moment I was aware of my talent
                > memorising the squares up to 1.000 went more or less automatically. I
                > started with 1 and by addibng I came up to 1.000. My memory must be a
                > very good one: they are still there.
                >
                > In the same way the cubes up to 100.
                >
                > All the multiplications of 2 digit numbers were there from about my 9th
                > year.
                >
                >
                >
                > This is not very impressive, but with good algoritms one can do a lot more.
                >
                >
                >
                > I am not perfect in it, but can do – owing to the cross method which taught
                > me Wim Klein – multiplications of 8 digit numbers.
                >
                >
                >
                > Jan van Koningsveld and Robert Fountain taught me decimal roots, and owing
                > tot hat knowledge I can do them , besides integer roots up to about 18
                > digits.
                >
                > Andy Robertshaw told interesting things about decimal cube roots.
                >
                >
                >
                > Having found the structure in the cubes I created an algortim and so can do
                > integer cube roots up to 24 digits.
                >
                >
                >
                > I have no idea what to do with x-decimals of pi.
                >
                > Last year I learnt the logaritms up to 100. They are gone because of
                > neglecting. But surely they are helpful in decimal roots, especially the
                > deep ones.
                >
                >
                >
                > For the younger ones amongst us I give the advise: consider which
                > possibilities there are in what you intend to do and then decide what you
                > want to memorise.
                >
                >
                >
                > Memorising "blindly" a lot of numbers is not very creative, so think very
                > well before beginning "a hell of a job".
                >
                >
                >
                >
                >
                >
                >
                > Kindest regards,
                >
                >
                >
                >
                >
                > Willem Bouman
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                >
                > Van: MentalCalculation@yahoogroups.com
                > [mailto:MentalCalculation@yahoogroups.com] Namens Retothejuggler
                > Verzonden: woensdag 5 december 2012 12:13
                > Aan: MentalCalculation@yahoogroups.com
                > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
                > "trivial entertainment"
                >
                >
                >
                >
                >
                > I`m wondering what other numbers friends here have stored in their minds, my
                > lame work is just 2-digit squares, 20 decimals of Pi, cubes up to 30 and
                > fith up to 12 right now and some primes...
                >
                > But I`m just back in it...there is hope...
                >
                > --- In MentalCalculation@yahoogroups.com
                > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
                > <dacastro123@> wrote:
                > >
                > > That's why I like math! There's a reason for everything, there are
                > patterns everywhere..
                > >
                > > I'm 19 years old. Memorizing 1000 squares is very impressive! When I was
                > 6, I memorized the first 20 powers of 2, but that's not really impressive...
                > >
                > > Cheers,
                > >
                > > Daniel
                > >
                > > --- In MentalCalculation@yahoogroups.com
                > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
                > <awap.bouman@> wrote:
                > > >
                > > > Dear Daniel,
                > > >
                > > >
                > > >
                > > > Well, I am a Dutchman, so neither native English speaker. But all you
                > > > write, I understand. By the way: 38 and 62 end on 44, but also do 12 and
                > 88.
                > > > The difference is in the hundreds. This concerns all the squares of the
                > even
                > > > numbers. See eg 08 and 92, squared 64 and 8464, EH ( even Hundreds) and
                > 42
                > > > and 58 squared resp. 1746 and 3364 OH (Odd Hundreds).
                > > >
                > > >
                > > >
                > > > In the squares of the odd numbers you'll see that the hundreds keep
                > their
                > > > nature. EG 13²=169, 37²=1369, 63²=3969, 87²=7569, all OH, odd hundreds.
                > > > Later on when you study the 3 digit squares, you'll see even thousands
                > and
                > > > odd thousands.
                > > >
                > > > Eg 13²=169, ET ( Even Thousand), 237²=56169 (ET), 263²=69169,
                > 487²=237169,
                > > > both OT, 513²=263169 and 737²=543169, both OT, 763²=582169 and
                > > > 987²=974169, both ET.
                > > >
                > > > Besides you can see 13+987=1000, 237+763=1000 etc.
                > > >
                > > >
                > > >
                > > > All the best with your number studies and have fun wit hit!!!!!
                > > >
                > > >
                > > >
                > > > I do not know how old you are. Concerning myself: at 14 I knew all the
                > > > squares up to 1000 and shortly after that all the cubes up to 100. With
                > that
                > > > I can do a lot of things.
                > > >
                > > >
                > > >
                > > >
                > > >
                > > > Kindest regards,
                > > >
                > > >
                > > >
                > > >
                > > >
                > > > Willem Bouman
                > > >
                > > >
                > > >
                > > >
                > > >
                > > >
                > > >
                > > >
                > > >
                > > >
                > > >
                > > >
                > > >
                > > >
                > > >
                > > >
                > > >
                > > > Van: MentalCalculation@yahoogroups.com
                > <mailto:MentalCalculation%40yahoogroups.com>
                > > > [mailto:MentalCalculation@yahoogroups.com
                > <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
                > > > Verzonden: zondag 2 december 2012 1:39
                > > > Aan: MentalCalculation@yahoogroups.com
                > <mailto:MentalCalculation%40yahoogroups.com>
                > > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
                > > > "trivial entertainment"
                > > >
                > > >
                > > >
                > > >
                > > >
                > > > I'm sorry Mr. Bouman, my name is Daniel.
                > > >
                > > > These are nice properties! While memorizing the squares I observed that
                > > > numbers that add up to 100 have their squares with the same ending, for
                > > > example 38 and 62. Both add up to a hundred. 38 squared is 1444 and 62
                > > > squared is 3844, so the last to digits match.
                > > >
                > > > Mnemonic is anything that can help memorizing something. It might be a
                > word,
                > > > a phrase or mental image that facilitate the process of memorizing.
                > > >
                > > > Well the squares are useful to me in multiplications, square roots and
                > they
                > > > also help to square larger numbers. The other powers I would like to
                > > > memorize because I think it's fun :)
                > > >
                > > > Sorry if my english is bad. I'm from Brazil.
                > > >
                > > > Thank You
                > > >
                > > > --- In MentalCalculation@yahoogroups.com
                > <mailto:MentalCalculation%40yahoogroups.com>
                > > > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
                > > > <awap.bouman@> wrote:
                > > > >
                > > > > Dear Mr. Dacastro93, or whom you may be,
                > > > >
                > > > >
                > > > >
                > > > > You could consider to subdivide the squares in groups with the same
                > last
                > > > > digits, so from 1-100 you can do 1,49,51 and 99, all their squares end
                > on
                > > > > 01. Then you take 2,48,52 and 98, all their squares ending on 04.
                > > > >
                > > > >
                > > > >
                > > > > What I did as a school boy during the less interesting lessons, is
                > writing
                > > > > all the numbers 1 up to 1.000 on a list and calculated the squares by
                > > > > adding: 2² =1 + (2+1)=4, 3²= 4 +(2+3)=9.
                > > > >
                > > > >
                > > > >
                > > > > 670²=448900, 671²= 448900 + (670+671) = 450241.
                > > > >
                > > > >
                > > > >
                > > > > For the cubes: look after the structure. The tens increase according
                > to-
                > > > if
                > > > > I am well informed - the iterationn of Newton.
                > > > >
                > > > > For 11 the increase of the tens is (3×1²×10) = 30 per ten, and indeed
                > 11³=
                > > > > 1331. For 21 the increase is 2×(3×1²×10) = 60, and indeed 21³ = 9261.
                > You
                > > > > have not everything, but there is a beginning.
                > > > >
                > > > >
                > > > >
                > > > > The following, still free of charge:
                > > > >
                > > > > 7³=343. IUncrease of the tens: 3×7²×10=70. Take 27³. Increase of the
                > tens
                > > > > 2×70= 40. So the last digits of 27³ have to end on 83. And indeed 27³=
                > > > > 19683.
                > > > >
                > > > >
                > > > >
                > > > > As I have not the faintest idea of what mnmonics are, I cannot help
                > you
                > > > with
                > > > > them.
                > > > >
                > > > >
                > > > >
                > > > > Did you consider what to do with the numbers you want to know by
                > heart?
                > > > >
                > > > >
                > > > >
                > > > >
                > > > >
                > > > > Kindest regards,
                > > > >
                > > > >
                > > > >
                > > > >
                > > > >
                > > > > Willem Bouman
                > > > >
                > > > >
                > > > >
                > > > >
                > > > >
                > > > >
                > > > >
                > > > >
                > > > >
                > > > > Van: MentalCalculation@yahoogroups.com
                > <mailto:MentalCalculation%40yahoogroups.com>
                > > > <mailto:MentalCalculation%40yahoogroups.com>
                > > > > [mailto:MentalCalculation@yahoogroups.com
                > <mailto:MentalCalculation%40yahoogroups.com>
                > > > <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
                > > > > Verzonden: woensdag 28 november 2012 12:42
                > > > > Aan: MentalCalculation@yahoogroups.com
                > <mailto:MentalCalculation%40yahoogroups.com>
                > > > <mailto:MentalCalculation%40yahoogroups.com>
                > > > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this
                > under
                > > > > "trivial entertainment"
                > > > >
                > > > >
                > > > >
                > > > >
                > > > >
                > > > > That was fun!
                > > > >
                > > > > The first 100 squares I memorized without the help of mnemonics. How
                > long
                > > > > can I go without mnemonics? I think I might try the first 100 cubes by
                > > > rote
                > > > > memorization, just like I did with the squares..
                > > > >
                > > > > Cheers
                > > > >
                > > > > --- In MentalCalculation@yahoogroups.com
                > <mailto:MentalCalculation%40yahoogroups.com>
                > > > <mailto:MentalCalculation%40yahoogroups.com>
                > > > > <mailto:MentalCalculation%40yahoogroups.com> , "Jerry" <wholphin48@>
                > > > > wrote:
                > > > > >
                > > > > >
                > > > > > Here's a way to show the result of some great calculating with no
                > > > work...
                > > > > >
                > > > > > Suppose a,b are positive integers, then you can write a^b in base a
                > > > > precisely
                > > > > > as a 1 followed by b zeros...
                > > > > >
                > > > > > For example 6^8 in base six is 100000000 That doesn't mean you have
                > a
                > > > clue
                > > > > what that number is in base ten, the usual reference. But you have
                > > > expressed
                > > > > the result in base six precisely and instantly. However, this time I
                > can
                > > > > tell you that 6^8 in base ten is equal to 1,679,616 :)
                > > > > >
                > > > > > Good luck with the mnemonics. I just thought this trivia might give
                > you
                > > > > all a humorous break!!
                > > > > >
                > > > > > Jerry Newport Tucson, AZ
                > > > > >
                > > > > > --- In MentalCalculation@yahoogroups.com
                > <mailto:MentalCalculation%40yahoogroups.com>
                > > > <mailto:MentalCalculation%40yahoogroups.com>
                > > > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
                > <dacastro123@>
                > > > > wrote:
                > > > > > >
                > > > > > > Interesting! Like I said..I'll try to memorize the cubes of 1-100,
                > > > then
                > > > > I will come up with a mnemonic system in order to commit to memory
                > higher
                > > > > powers. Let's see what I can do.
                > > > > > >
                > > > > > > Cheers,
                > > > > > >
                > > > > > > Daniel
                > > > > > >
                > > > > > > --- In MentalCalculation@yahoogroups.com
                > <mailto:MentalCalculation%40yahoogroups.com>
                > > > <mailto:MentalCalculation%40yahoogroups.com>
                > > > > <mailto:MentalCalculation%40yahoogroups.com> , "Retothejuggler"
                > > > > <retothejuggler@> wrote:
                > > > > > > >
                > > > > > > > In the last months, I quit mental calculation a bit and switched
                > > > over
                > > > > to sudoku and logical puzzle solving. A few weeks ago my numbers
                > hunger
                > > > came
                > > > > back and alongside this I found an older scientific article about
                > Rüdiger
                > > > > Gamm.
                > > > > > > >
                > > > > > > > Well, he learned the higher powers but still claims to construct
                > > > > powers out of known powers, no idea about how.
                > > > > > > >
                > > > > > > > If you want to know what can be calculated, history shows:
                > > > > > > >
                > > > > > > > Mlle Osaka, 2 digits up to the 10.th (probably from memory), 3
                > > > digits
                > > > > up to 8th.
                > > > > > > >
                > > > > > > > Oscar Verhaeghe 9 999 999 to the 5th., 40 seconds
                > > > > > > >
                > > > > > > > Marathe one digit up to the 20.th (probably from memory)
                > > > > > > >
                > > > > > > > Klein calculated a 16th.
                > > > > > > >
                > > > > > > > Any mnemonic armed and aarithemtic skilled person can do higher
                > ones
                > > > > but not in a matter of seconds.
                > > > > > > >
                > > > > > > > Thanks Ron again for our offline discussion.
                > > > > > > >
                > > > > > > >
                > > > > > > >
                > > > > > > > --- In MentalCalculation@yahoogroups.com
                > <mailto:MentalCalculation%40yahoogroups.com>
                > > > <mailto:MentalCalculation%40yahoogroups.com>
                > > > > <mailto:MentalCalculation%40yahoogroups.com> , "rondrond1" <doerfpub@>
                > > > > wrote:
                > > > > > > > >
                > > > > > > > > That's a very good question. Reto and I have discussed this
                > > > offline
                > > > > in the past, and we did not come up with a good solution for high
                > powers.
                > > > I
                > > > > believe the number of significant digits of the logarithm would have
                > to
                > > > > equal the number of significant digits of the solution, although the
                > last
                > > > > few digits of the answer might be found from the last few digits of
                > the
                > > > > problem and also two of the digits can be found from 99-remainder (mod
                > 99)
                > > > > calculations if the rest of the digits are known. R�diger Gamm would
                > > > > probably have memorized high powers, although I can't definitively say
                > > > that
                > > > > since I don't know the method or methods he uses.
                > > > > > > > >
                > > > > > > > > Ron
                > > > > > > > >
                > > > > > > > > --- In MentalCalculation@yahoogroups.com
                > <mailto:MentalCalculation%40yahoogroups.com>
                > > > <mailto:MentalCalculation%40yahoogroups.com>
                > > > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
                > <dacastro123@>
                > > > > wrote:
                > > > > > > > > >
                > > > > > > > > > Hi! I have a question for you...
                > > > > > > > > >
                > > > > > > > > > How can I calculate mentally high powers like, for example
                > > > 41^23?
                > > > > > > > > >
                > > > > > > > > > I read that it can be achivied using logs, but the result
                > will
                > > > not
                > > > > be accurate: log41 ~ 1,6128, so log 41^23 will be 37,0944. Doing 41^23
                > in
                > > > a
                > > > > calculator: =1,241734 x 10^37, but, with the use of antilog, I get
                > 1,24280
                > > > x
                > > > > 10^37. How can I find precisely every single digit of the power? How
                > many
                > > > > decimal places of logs will I need?
                > > > > > > > > >
                > > > > > > > > > And what about R�diger Gamm? Does he really have memorized
                > the
                > > > > powers? Does he use mnemonics?
                > > > > > > > > >
                > > > > > > > > > Thank You in advance
                > > > > > > > > >
                > > > > > > > >
                > > > > > > >
                > > > > > >
                > > > > >
                > > > >
                > > > >
                > > > >
                > > > >
                > > > >
                > > > > [Non-text portions of this message have been removed]
                > > > >
                > > >
                > > >
                > > >
                > > >
                > > >
                > > > [Non-text portions of this message have been removed]
                > > >
                > >
                >
                >
                >
                >
                >
                > [Non-text portions of this message have been removed]
                >
              • A.W.A.P. Bouman
                Hi Reto and fellow calculators, It is a pity, Reto, but you are right. And indeed getting confident with the cubes develops along aonther path. But that does
                Message 7 of 24 , Dec 6, 2012
                • 0 Attachment
                  Hi Reto and fellow calculators,



                  It is a pity, Reto, but you are right. And indeed getting confident with the
                  cubes develops along aonther path.

                  But that does not mean that there is no structure in the cubes. The tens
                  increase according to Newtons iteration.

                  Let’s start with 11. There the tens increase with 10 in comparison with 1.
                  And the tens increase according to Newton as follows 3×1²×10, so with 30.
                  And indeed 11³= 11 31, 21³ = 92 61



                  3³ = 27 and the trens of the cubes increase with 3×3²×10= 70. And look 13³ =
                  21 97, 23³ = 121 67. The best way to get confident is to calculate them
                  yourself, rather than to take a stupid machine.



                  Mnemonics: I read from other calculators that they associate numbers with:
                  rooms in the house, pictures, you name it. I do



                  it all without and have no idea how my memory works. I can only say that the
                  results are good. And are greatful fort hat.



                  Kindest regards,





                  Willem Bouman

















                  Van: MentalCalculation@yahoogroups.com
                  [mailto:MentalCalculation@yahoogroups.com] Namens Retothejuggler
                  Verzonden: donderdag 6 december 2012 13:59
                  Aan: MentalCalculation@yahoogroups.com
                  Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
                  "trivial entertainment"





                  Dear Willem

                  How have you calculated the cubes? They can`t be broken down simply in a row
                  of additions (which you used to learn squares).

                  It would be interesting to see your skills in memorizing numbers without
                  mnemotechnic pictures.

                  You`re doing this for years and are miles away from most, but I`ll choose my
                  numbers carefully :-).

                  Pi is just for fun.

                  Thanks for your input.

                  Greetings Reto

                  --- In MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
                  <awap.bouman@...> wrote:
                  >
                  > Dear fellow calculators,
                  >
                  >
                  >
                  > What should be in someones memory? At the moment I was aware of my talent
                  > memorising the squares up to 1.000 went more or less automatically. I
                  > started with 1 and by addibng I came up to 1.000. My memory must be a
                  > very good one: they are still there.
                  >
                  > In the same way the cubes up to 100.
                  >
                  > All the multiplications of 2 digit numbers were there from about my 9th
                  > year.
                  >
                  >
                  >
                  > This is not very impressive, but with good algoritms one can do a lot
                  more.
                  >
                  >
                  >
                  > I am not perfect in it, but can do – owing to the cross method which
                  taught
                  > me Wim Klein – multiplications of 8 digit numbers.
                  >
                  >
                  >
                  > Jan van Koningsveld and Robert Fountain taught me decimal roots, and owing
                  > tot hat knowledge I can do them , besides integer roots up to about 18
                  > digits.
                  >
                  > Andy Robertshaw told interesting things about decimal cube roots.
                  >
                  >
                  >
                  > Having found the structure in the cubes I created an algortim and so can
                  do
                  > integer cube roots up to 24 digits.
                  >
                  >
                  >
                  > I have no idea what to do with x-decimals of pi.
                  >
                  > Last year I learnt the logaritms up to 100. They are gone because of
                  > neglecting. But surely they are helpful in decimal roots, especially the
                  > deep ones.
                  >
                  >
                  >
                  > For the younger ones amongst us I give the advise: consider which
                  > possibilities there are in what you intend to do and then decide what you
                  > want to memorise.
                  >
                  >
                  >
                  > Memorising "blindly" a lot of numbers is not very creative, so think very
                  > well before beginning "a hell of a job".
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  > Kindest regards,
                  >
                  >
                  >
                  >
                  >
                  > Willem Bouman
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  > Van: MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com>
                  > [mailto:MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com> ] Namens Retothejuggler
                  > Verzonden: woensdag 5 december 2012 12:13
                  > Aan: MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com>
                  > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
                  > "trivial entertainment"
                  >
                  >
                  >
                  >
                  >
                  > I`m wondering what other numbers friends here have stored in their minds,
                  my
                  > lame work is just 2-digit squares, 20 decimals of Pi, cubes up to 30 and
                  > fith up to 12 right now and some primes...
                  >
                  > But I`m just back in it...there is hope...
                  >
                  > --- In MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com>
                  > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
                  > <dacastro123@> wrote:
                  > >
                  > > That's why I like math! There's a reason for everything, there are
                  > patterns everywhere..
                  > >
                  > > I'm 19 years old. Memorizing 1000 squares is very impressive! When I was
                  > 6, I memorized the first 20 powers of 2, but that's not really
                  impressive...
                  > >
                  > > Cheers,
                  > >
                  > > Daniel
                  > >
                  > > --- In MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com>
                  > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
                  > <awap.bouman@> wrote:
                  > > >
                  > > > Dear Daniel,
                  > > >
                  > > >
                  > > >
                  > > > Well, I am a Dutchman, so neither native English speaker. But all you
                  > > > write, I understand. By the way: 38 and 62 end on 44, but also do 12
                  and
                  > 88.
                  > > > The difference is in the hundreds. This concerns all the squares of
                  the
                  > even
                  > > > numbers. See eg 08 and 92, squared 64 and 8464, EH ( even Hundreds)
                  and
                  > 42
                  > > > and 58 squared resp. 1746 and 3364 OH (Odd Hundreds).
                  > > >
                  > > >
                  > > >
                  > > > In the squares of the odd numbers you'll see that the hundreds keep
                  > their
                  > > > nature. EG 13²=169, 37²=1369, 63²=3969, 87²=7569, all OH, odd
                  hundreds.
                  > > > Later on when you study the 3 digit squares, you'll see even thousands
                  > and
                  > > > odd thousands.
                  > > >
                  > > > Eg 13²=169, ET ( Even Thousand), 237²=56169 (ET), 263²=69169,
                  > 487²=237169,
                  > > > both OT, 513²=263169 and 737²=543169, both OT, 763²=582169 and
                  > > > 987²=974169, both ET.
                  > > >
                  > > > Besides you can see 13+987=1000, 237+763=1000 etc.
                  > > >
                  > > >
                  > > >
                  > > > All the best with your number studies and have fun wit hit!!!!!
                  > > >
                  > > >
                  > > >
                  > > > I do not know how old you are. Concerning myself: at 14 I knew all the
                  > > > squares up to 1000 and shortly after that all the cubes up to 100.
                  With
                  > that
                  > > > I can do a lot of things.
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > > Kindest regards,
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > > Willem Bouman
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > > Van: MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com>
                  > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > [mailto:MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com>
                  > <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
                  > > > Verzonden: zondag 2 december 2012 1:39
                  > > > Aan: MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com>
                  > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this
                  under
                  > > > "trivial entertainment"
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > > I'm sorry Mr. Bouman, my name is Daniel.
                  > > >
                  > > > These are nice properties! While memorizing the squares I observed
                  that
                  > > > numbers that add up to 100 have their squares with the same ending,
                  for
                  > > > example 38 and 62. Both add up to a hundred. 38 squared is 1444 and 62
                  > > > squared is 3844, so the last to digits match.
                  > > >
                  > > > Mnemonic is anything that can help memorizing something. It might be a
                  > word,
                  > > > a phrase or mental image that facilitate the process of memorizing.
                  > > >
                  > > > Well the squares are useful to me in multiplications, square roots and
                  > they
                  > > > also help to square larger numbers. The other powers I would like to
                  > > > memorize because I think it's fun :)
                  > > >
                  > > > Sorry if my english is bad. I'm from Brazil.
                  > > >
                  > > > Thank You
                  > > >
                  > > > --- In MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com>
                  > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
                  > > > <awap.bouman@> wrote:
                  > > > >
                  > > > > Dear Mr. Dacastro93, or whom you may be,
                  > > > >
                  > > > >
                  > > > >
                  > > > > You could consider to subdivide the squares in groups with the same
                  > last
                  > > > > digits, so from 1-100 you can do 1,49,51 and 99, all their squares
                  end
                  > on
                  > > > > 01. Then you take 2,48,52 and 98, all their squares ending on 04.
                  > > > >
                  > > > >
                  > > > >
                  > > > > What I did as a school boy during the less interesting lessons, is
                  > writing
                  > > > > all the numbers 1 up to 1.000 on a list and calculated the squares
                  by
                  > > > > adding: 2² =1 + (2+1)=4, 3²= 4 +(2+3)=9.
                  > > > >
                  > > > >
                  > > > >
                  > > > > 670²=448900, 671²= 448900 + (670+671) = 450241.
                  > > > >
                  > > > >
                  > > > >
                  > > > > For the cubes: look after the structure. The tens increase according
                  > to-
                  > > > if
                  > > > > I am well informed - the iterationn of Newton.
                  > > > >
                  > > > > For 11 the increase of the tens is (3×1²×10) = 30 per ten, and
                  indeed
                  > 11³=
                  > > > > 1331. For 21 the increase is 2×(3×1²×10) = 60, and indeed 21³ =
                  9261.
                  > You
                  > > > > have not everything, but there is a beginning.
                  > > > >
                  > > > >
                  > > > >
                  > > > > The following, still free of charge:
                  > > > >
                  > > > > 7³=343. IUncrease of the tens: 3×7²×10=70. Take 27³. Increase of the
                  > tens
                  > > > > 2×70= 40. So the last digits of 27³ have to end on 83. And indeed
                  27³=
                  > > > > 19683.
                  > > > >
                  > > > >
                  > > > >
                  > > > > As I have not the faintest idea of what mnmonics are, I cannot help
                  > you
                  > > > with
                  > > > > them.
                  > > > >
                  > > > >
                  > > > >
                  > > > > Did you consider what to do with the numbers you want to know by
                  > heart?
                  > > > >
                  > > > >
                  > > > >
                  > > > >
                  > > > >
                  > > > > Kindest regards,
                  > > > >
                  > > > >
                  > > > >
                  > > > >
                  > > > >
                  > > > > Willem Bouman
                  > > > >
                  > > > >
                  > > > >
                  > > > >
                  > > > >
                  > > > >
                  > > > >
                  > > > >
                  > > > >
                  > > > > Van: MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com>
                  > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > > [mailto:MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com>
                  > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
                  > > > > Verzonden: woensdag 28 november 2012 12:42
                  > > > > Aan: MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com>
                  > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this
                  > under
                  > > > > "trivial entertainment"
                  > > > >
                  > > > >
                  > > > >
                  > > > >
                  > > > >
                  > > > > That was fun!
                  > > > >
                  > > > > The first 100 squares I memorized without the help of mnemonics. How
                  > long
                  > > > > can I go without mnemonics? I think I might try the first 100 cubes
                  by
                  > > > rote
                  > > > > memorization, just like I did with the squares..
                  > > > >
                  > > > > Cheers
                  > > > >
                  > > > > --- In MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com>
                  > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > > <mailto:MentalCalculation%40yahoogroups.com> , "Jerry" <wholphin48@>
                  > > > > wrote:
                  > > > > >
                  > > > > >
                  > > > > > Here's a way to show the result of some great calculating with no
                  > > > work...
                  > > > > >
                  > > > > > Suppose a,b are positive integers, then you can write a^b in base
                  a
                  > > > > precisely
                  > > > > > as a 1 followed by b zeros...
                  > > > > >
                  > > > > > For example 6^8 in base six is 100000000 That doesn't mean you
                  have
                  > a
                  > > > clue
                  > > > > what that number is in base ten, the usual reference. But you have
                  > > > expressed
                  > > > > the result in base six precisely and instantly. However, this time I
                  > can
                  > > > > tell you that 6^8 in base ten is equal to 1,679,616 :)
                  > > > > >
                  > > > > > Good luck with the mnemonics. I just thought this trivia might
                  give
                  > you
                  > > > > all a humorous break!!
                  > > > > >
                  > > > > > Jerry Newport Tucson, AZ
                  > > > > >
                  > > > > > --- In MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com>
                  > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
                  > <dacastro123@>
                  > > > > wrote:
                  > > > > > >
                  > > > > > > Interesting! Like I said..I'll try to memorize the cubes of
                  1-100,
                  > > > then
                  > > > > I will come up with a mnemonic system in order to commit to memory
                  > higher
                  > > > > powers. Let's see what I can do.
                  > > > > > >
                  > > > > > > Cheers,
                  > > > > > >
                  > > > > > > Daniel
                  > > > > > >
                  > > > > > > --- In MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com>
                  > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > > <mailto:MentalCalculation%40yahoogroups.com> , "Retothejuggler"
                  > > > > <retothejuggler@> wrote:
                  > > > > > > >
                  > > > > > > > In the last months, I quit mental calculation a bit and
                  switched
                  > > > over
                  > > > > to sudoku and logical puzzle solving. A few weeks ago my numbers
                  > hunger
                  > > > came
                  > > > > back and alongside this I found an older scientific article about
                  > Rüdiger
                  > > > > Gamm.
                  > > > > > > >
                  > > > > > > > Well, he learned the higher powers but still claims to
                  construct
                  > > > > powers out of known powers, no idea about how.
                  > > > > > > >
                  > > > > > > > If you want to know what can be calculated, history shows:
                  > > > > > > >
                  > > > > > > > Mlle Osaka, 2 digits up to the 10.th (probably from memory), 3
                  > > > digits
                  > > > > up to 8th.
                  > > > > > > >
                  > > > > > > > Oscar Verhaeghe 9 999 999 to the 5th., 40 seconds
                  > > > > > > >
                  > > > > > > > Marathe one digit up to the 20.th (probably from memory)
                  > > > > > > >
                  > > > > > > > Klein calculated a 16th.
                  > > > > > > >
                  > > > > > > > Any mnemonic armed and aarithemtic skilled person can do
                  higher
                  > ones
                  > > > > but not in a matter of seconds.
                  > > > > > > >
                  > > > > > > > Thanks Ron again for our offline discussion.
                  > > > > > > >
                  > > > > > > >
                  > > > > > > >
                  > > > > > > > --- In MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com>
                  > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > > <mailto:MentalCalculation%40yahoogroups.com> , "rondrond1"
                  <doerfpub@>
                  > > > > wrote:
                  > > > > > > > >
                  > > > > > > > > That's a very good question. Reto and I have discussed this
                  > > > offline
                  > > > > in the past, and we did not come up with a good solution for high
                  > powers.
                  > > > I
                  > > > > believe the number of significant digits of the logarithm would have
                  > to
                  > > > > equal the number of significant digits of the solution, although the
                  > last
                  > > > > few digits of the answer might be found from the last few digits of
                  > the
                  > > > > problem and also two of the digits can be found from 99-remainder
                  (mod
                  > 99)
                  > > > > calculations if the rest of the digits are known. R�diger Gamm
                  would
                  > > > > probably have memorized high powers, although I can't definitively
                  say
                  > > > that
                  > > > > since I don't know the method or methods he uses.
                  > > > > > > > >
                  > > > > > > > > Ron
                  > > > > > > > >
                  > > > > > > > > --- In MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com>
                  > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > <mailto:MentalCalculation%40yahoogroups.com>
                  > > > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
                  > <dacastro123@>
                  > > > > wrote:
                  > > > > > > > > >
                  > > > > > > > > > Hi! I have a question for you...
                  > > > > > > > > >
                  > > > > > > > > > How can I calculate mentally high powers like, for example
                  > > > 41^23?
                  > > > > > > > > >
                  > > > > > > > > > I read that it can be achivied using logs, but the result
                  > will
                  > > > not
                  > > > > be accurate: log41 ~ 1,6128, so log 41^23 will be 37,0944. Doing
                  41^23
                  > in
                  > > > a
                  > > > > calculator: =1,241734 x 10^37, but, with the use of antilog, I get
                  > 1,24280
                  > > > x
                  > > > > 10^37. How can I find precisely every single digit of the power? How
                  > many
                  > > > > decimal places of logs will I need?
                  > > > > > > > > >
                  > > > > > > > > > And what about R�diger Gamm? Does he really have
                  memorized
                  > the
                  > > > > powers? Does he use mnemonics?
                  > > > > > > > > >
                  > > > > > > > > > Thank You in advance
                  > > > > > > > > >
                  > > > > > > > >
                  > > > > > > >
                  > > > > > >
                  > > > > >
                  > > > >
                  > > > >
                  > > > >
                  > > > >
                  > > > >
                  > > > > [Non-text portions of this message have been removed]
                  > > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > >
                  > > > [Non-text portions of this message have been removed]
                  > > >
                  > >
                  >
                  >
                  >
                  >
                  >
                  > [Non-text portions of this message have been removed]
                  >





                  [Non-text portions of this message have been removed]
                • dacastro93
                  About your memory...do You hear the numbers or do You see them in your head? How many times have You repeated the 1000 squares before getting them stucked into
                  Message 8 of 24 , Dec 10, 2012
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                    About your memory...do You hear the numbers or do You see them in your head? How many times have You repeated the 1000 squares before getting them stucked into your memory? I calculate them while walking with my dog and repeat 2 to 3 times before memorizing, but I do review in the next day. To calculate squares, what method is used? Binomial expansion? Because I'm doing with the method I saw on Arthur Benjamin's book. For example 257^2, I do 200x314 + 57^2. Is this the fastest method?

                    Thanks in advance,

                    Daniel

                    --- In MentalCalculation@yahoogroups.com, "A.W.A.P. Bouman" <awap.bouman@...> wrote:
                    >
                    > Hi Reto and fellow calculators,
                    >
                    >
                    >
                    > It is a pity, Reto, but you are right. And indeed getting confident with the
                    > cubes develops along aonther path.
                    >
                    > But that does not mean that there is no structure in the cubes. The tens
                    > increase according to Newtons iteration.
                    >
                    > Let's start with 11. There the tens increase with 10 in comparison with 1.
                    > And the tens increase according to Newton as follows 3×1²×10, so with 30.
                    > And indeed 11³= 11 31, 21³ = 92 61
                    >
                    >
                    >
                    > 3³ = 27 and the trens of the cubes increase with 3×3²×10= 70. And look 13³ =
                    > 21 97, 23³ = 121 67. The best way to get confident is to calculate them
                    > yourself, rather than to take a stupid machine.
                    >
                    >
                    >
                    > Mnemonics: I read from other calculators that they associate numbers with:
                    > rooms in the house, pictures, you name it. I do
                    >
                    >
                    >
                    > it all without and have no idea how my memory works. I can only say that the
                    > results are good. And are greatful fort hat.
                    >
                    >
                    >
                    > Kindest regards,
                    >
                    >
                    >
                    >
                    >
                    > Willem Bouman
                    >
                    >
                    >
                    >
                    >
                    >
                    >
                    >
                    >
                    >
                    >
                    >
                    >
                    >
                    >
                    >
                    >
                    > Van: MentalCalculation@yahoogroups.com
                    > [mailto:MentalCalculation@yahoogroups.com] Namens Retothejuggler
                    > Verzonden: donderdag 6 december 2012 13:59
                    > Aan: MentalCalculation@yahoogroups.com
                    > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
                    > "trivial entertainment"
                    >
                    >
                    >
                    >
                    >
                    > Dear Willem
                    >
                    > How have you calculated the cubes? They can`t be broken down simply in a row
                    > of additions (which you used to learn squares).
                    >
                    > It would be interesting to see your skills in memorizing numbers without
                    > mnemotechnic pictures.
                    >
                    > You`re doing this for years and are miles away from most, but I`ll choose my
                    > numbers carefully :-).
                    >
                    > Pi is just for fun.
                    >
                    > Thanks for your input.
                    >
                    > Greetings Reto
                    >
                    > --- In MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
                    > <awap.bouman@> wrote:
                    > >
                    > > Dear fellow calculators,
                    > >
                    > >
                    > >
                    > > What should be in someones memory? At the moment I was aware of my talent
                    > > memorising the squares up to 1.000 went more or less automatically. I
                    > > started with 1 and by addibng I came up to 1.000. My memory must be a
                    > > very good one: they are still there.
                    > >
                    > > In the same way the cubes up to 100.
                    > >
                    > > All the multiplications of 2 digit numbers were there from about my 9th
                    > > year.
                    > >
                    > >
                    > >
                    > > This is not very impressive, but with good algoritms one can do a lot
                    > more.
                    > >
                    > >
                    > >
                    > > I am not perfect in it, but can do – owing to the cross method which
                    > taught
                    > > me Wim Klein – multiplications of 8 digit numbers.
                    > >
                    > >
                    > >
                    > > Jan van Koningsveld and Robert Fountain taught me decimal roots, and owing
                    > > tot hat knowledge I can do them , besides integer roots up to about 18
                    > > digits.
                    > >
                    > > Andy Robertshaw told interesting things about decimal cube roots.
                    > >
                    > >
                    > >
                    > > Having found the structure in the cubes I created an algortim and so can
                    > do
                    > > integer cube roots up to 24 digits.
                    > >
                    > >
                    > >
                    > > I have no idea what to do with x-decimals of pi.
                    > >
                    > > Last year I learnt the logaritms up to 100. They are gone because of
                    > > neglecting. But surely they are helpful in decimal roots, especially the
                    > > deep ones.
                    > >
                    > >
                    > >
                    > > For the younger ones amongst us I give the advise: consider which
                    > > possibilities there are in what you intend to do and then decide what you
                    > > want to memorise.
                    > >
                    > >
                    > >
                    > > Memorising "blindly" a lot of numbers is not very creative, so think very
                    > > well before beginning "a hell of a job".
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > > Kindest regards,
                    > >
                    > >
                    > >
                    > >
                    > >
                    > > Willem Bouman
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > > Van: MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com>
                    > > [mailto:MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com> ] Namens Retothejuggler
                    > > Verzonden: woensdag 5 december 2012 12:13
                    > > Aan: MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com>
                    > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
                    > > "trivial entertainment"
                    > >
                    > >
                    > >
                    > >
                    > >
                    > > I`m wondering what other numbers friends here have stored in their minds,
                    > my
                    > > lame work is just 2-digit squares, 20 decimals of Pi, cubes up to 30 and
                    > > fith up to 12 right now and some primes...
                    > >
                    > > But I`m just back in it...there is hope...
                    > >
                    > > --- In MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com>
                    > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
                    > > <dacastro123@> wrote:
                    > > >
                    > > > That's why I like math! There's a reason for everything, there are
                    > > patterns everywhere..
                    > > >
                    > > > I'm 19 years old. Memorizing 1000 squares is very impressive! When I was
                    > > 6, I memorized the first 20 powers of 2, but that's not really
                    > impressive...
                    > > >
                    > > > Cheers,
                    > > >
                    > > > Daniel
                    > > >
                    > > > --- In MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com>
                    > > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
                    > > <awap.bouman@> wrote:
                    > > > >
                    > > > > Dear Daniel,
                    > > > >
                    > > > >
                    > > > >
                    > > > > Well, I am a Dutchman, so neither native English speaker. But all you
                    > > > > write, I understand. By the way: 38 and 62 end on 44, but also do 12
                    > and
                    > > 88.
                    > > > > The difference is in the hundreds. This concerns all the squares of
                    > the
                    > > even
                    > > > > numbers. See eg 08 and 92, squared 64 and 8464, EH ( even Hundreds)
                    > and
                    > > 42
                    > > > > and 58 squared resp. 1746 and 3364 OH (Odd Hundreds).
                    > > > >
                    > > > >
                    > > > >
                    > > > > In the squares of the odd numbers you'll see that the hundreds keep
                    > > their
                    > > > > nature. EG 13²=169, 37²=1369, 63²=3969, 87²=7569, all OH, odd
                    > hundreds.
                    > > > > Later on when you study the 3 digit squares, you'll see even thousands
                    > > and
                    > > > > odd thousands.
                    > > > >
                    > > > > Eg 13²=169, ET ( Even Thousand), 237²=56169 (ET), 263²=69169,
                    > > 487²=237169,
                    > > > > both OT, 513²=263169 and 737²=543169, both OT, 763²=582169 and
                    > > > > 987²=974169, both ET.
                    > > > >
                    > > > > Besides you can see 13+987=1000, 237+763=1000 etc.
                    > > > >
                    > > > >
                    > > > >
                    > > > > All the best with your number studies and have fun wit hit!!!!!
                    > > > >
                    > > > >
                    > > > >
                    > > > > I do not know how old you are. Concerning myself: at 14 I knew all the
                    > > > > squares up to 1000 and shortly after that all the cubes up to 100.
                    > With
                    > > that
                    > > > > I can do a lot of things.
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > > Kindest regards,
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > > Willem Bouman
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > > Van: MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com>
                    > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > [mailto:MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com>
                    > > <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
                    > > > > Verzonden: zondag 2 december 2012 1:39
                    > > > > Aan: MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com>
                    > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this
                    > under
                    > > > > "trivial entertainment"
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > > I'm sorry Mr. Bouman, my name is Daniel.
                    > > > >
                    > > > > These are nice properties! While memorizing the squares I observed
                    > that
                    > > > > numbers that add up to 100 have their squares with the same ending,
                    > for
                    > > > > example 38 and 62. Both add up to a hundred. 38 squared is 1444 and 62
                    > > > > squared is 3844, so the last to digits match.
                    > > > >
                    > > > > Mnemonic is anything that can help memorizing something. It might be a
                    > > word,
                    > > > > a phrase or mental image that facilitate the process of memorizing.
                    > > > >
                    > > > > Well the squares are useful to me in multiplications, square roots and
                    > > they
                    > > > > also help to square larger numbers. The other powers I would like to
                    > > > > memorize because I think it's fun :)
                    > > > >
                    > > > > Sorry if my english is bad. I'm from Brazil.
                    > > > >
                    > > > > Thank You
                    > > > >
                    > > > > --- In MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com>
                    > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
                    > > > > <awap.bouman@> wrote:
                    > > > > >
                    > > > > > Dear Mr. Dacastro93, or whom you may be,
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > > You could consider to subdivide the squares in groups with the same
                    > > last
                    > > > > > digits, so from 1-100 you can do 1,49,51 and 99, all their squares
                    > end
                    > > on
                    > > > > > 01. Then you take 2,48,52 and 98, all their squares ending on 04.
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > > What I did as a school boy during the less interesting lessons, is
                    > > writing
                    > > > > > all the numbers 1 up to 1.000 on a list and calculated the squares
                    > by
                    > > > > > adding: 2² =1 + (2+1)=4, 3²= 4 +(2+3)=9.
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > > 670²=448900, 671²= 448900 + (670+671) = 450241.
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > > For the cubes: look after the structure. The tens increase according
                    > > to-
                    > > > > if
                    > > > > > I am well informed - the iterationn of Newton.
                    > > > > >
                    > > > > > For 11 the increase of the tens is (3×1²×10) = 30 per ten, and
                    > indeed
                    > > 11³=
                    > > > > > 1331. For 21 the increase is 2×(3×1²×10) = 60, and indeed 21³ =
                    > 9261.
                    > > You
                    > > > > > have not everything, but there is a beginning.
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > > The following, still free of charge:
                    > > > > >
                    > > > > > 7³=343. IUncrease of the tens: 3×7²×10=70. Take 27³. Increase of the
                    > > tens
                    > > > > > 2×70= 40. So the last digits of 27³ have to end on 83. And indeed
                    > 27³=
                    > > > > > 19683.
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > > As I have not the faintest idea of what mnmonics are, I cannot help
                    > > you
                    > > > > with
                    > > > > > them.
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > > Did you consider what to do with the numbers you want to know by
                    > > heart?
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > > Kindest regards,
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > > Willem Bouman
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > > Van: MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com>
                    > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > > [mailto:MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com>
                    > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
                    > > > > > Verzonden: woensdag 28 november 2012 12:42
                    > > > > > Aan: MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com>
                    > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this
                    > > under
                    > > > > > "trivial entertainment"
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > > That was fun!
                    > > > > >
                    > > > > > The first 100 squares I memorized without the help of mnemonics. How
                    > > long
                    > > > > > can I go without mnemonics? I think I might try the first 100 cubes
                    > by
                    > > > > rote
                    > > > > > memorization, just like I did with the squares..
                    > > > > >
                    > > > > > Cheers
                    > > > > >
                    > > > > > --- In MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com>
                    > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > > <mailto:MentalCalculation%40yahoogroups.com> , "Jerry" <wholphin48@>
                    > > > > > wrote:
                    > > > > > >
                    > > > > > >
                    > > > > > > Here's a way to show the result of some great calculating with no
                    > > > > work...
                    > > > > > >
                    > > > > > > Suppose a,b are positive integers, then you can write a^b in base
                    > a
                    > > > > > precisely
                    > > > > > > as a 1 followed by b zeros...
                    > > > > > >
                    > > > > > > For example 6^8 in base six is 100000000 That doesn't mean you
                    > have
                    > > a
                    > > > > clue
                    > > > > > what that number is in base ten, the usual reference. But you have
                    > > > > expressed
                    > > > > > the result in base six precisely and instantly. However, this time I
                    > > can
                    > > > > > tell you that 6^8 in base ten is equal to 1,679,616 :)
                    > > > > > >
                    > > > > > > Good luck with the mnemonics. I just thought this trivia might
                    > give
                    > > you
                    > > > > > all a humorous break!!
                    > > > > > >
                    > > > > > > Jerry Newport Tucson, AZ
                    > > > > > >
                    > > > > > > --- In MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com>
                    > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
                    > > <dacastro123@>
                    > > > > > wrote:
                    > > > > > > >
                    > > > > > > > Interesting! Like I said..I'll try to memorize the cubes of
                    > 1-100,
                    > > > > then
                    > > > > > I will come up with a mnemonic system in order to commit to memory
                    > > higher
                    > > > > > powers. Let's see what I can do.
                    > > > > > > >
                    > > > > > > > Cheers,
                    > > > > > > >
                    > > > > > > > Daniel
                    > > > > > > >
                    > > > > > > > --- In MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com>
                    > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > > <mailto:MentalCalculation%40yahoogroups.com> , "Retothejuggler"
                    > > > > > <retothejuggler@> wrote:
                    > > > > > > > >
                    > > > > > > > > In the last months, I quit mental calculation a bit and
                    > switched
                    > > > > over
                    > > > > > to sudoku and logical puzzle solving. A few weeks ago my numbers
                    > > hunger
                    > > > > came
                    > > > > > back and alongside this I found an older scientific article about
                    > > Rüdiger
                    > > > > > Gamm.
                    > > > > > > > >
                    > > > > > > > > Well, he learned the higher powers but still claims to
                    > construct
                    > > > > > powers out of known powers, no idea about how.
                    > > > > > > > >
                    > > > > > > > > If you want to know what can be calculated, history shows:
                    > > > > > > > >
                    > > > > > > > > Mlle Osaka, 2 digits up to the 10.th (probably from memory), 3
                    > > > > digits
                    > > > > > up to 8th.
                    > > > > > > > >
                    > > > > > > > > Oscar Verhaeghe 9 999 999 to the 5th., 40 seconds
                    > > > > > > > >
                    > > > > > > > > Marathe one digit up to the 20.th (probably from memory)
                    > > > > > > > >
                    > > > > > > > > Klein calculated a 16th.
                    > > > > > > > >
                    > > > > > > > > Any mnemonic armed and aarithemtic skilled person can do
                    > higher
                    > > ones
                    > > > > > but not in a matter of seconds.
                    > > > > > > > >
                    > > > > > > > > Thanks Ron again for our offline discussion.
                    > > > > > > > >
                    > > > > > > > >
                    > > > > > > > >
                    > > > > > > > > --- In MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com>
                    > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > > <mailto:MentalCalculation%40yahoogroups.com> , "rondrond1"
                    > <doerfpub@>
                    > > > > > wrote:
                    > > > > > > > > >
                    > > > > > > > > > That's a very good question. Reto and I have discussed this
                    > > > > offline
                    > > > > > in the past, and we did not come up with a good solution for high
                    > > powers.
                    > > > > I
                    > > > > > believe the number of significant digits of the logarithm would have
                    > > to
                    > > > > > equal the number of significant digits of the solution, although the
                    > > last
                    > > > > > few digits of the answer might be found from the last few digits of
                    > > the
                    > > > > > problem and also two of the digits can be found from 99-remainder
                    > (mod
                    > > 99)
                    > > > > > calculations if the rest of the digits are known. R�diger Gamm
                    > would
                    > > > > > probably have memorized high powers, although I can't definitively
                    > say
                    > > > > that
                    > > > > > since I don't know the method or methods he uses.
                    > > > > > > > > >
                    > > > > > > > > > Ron
                    > > > > > > > > >
                    > > > > > > > > > --- In MentalCalculation@yahoogroups.com
                    > <mailto:MentalCalculation%40yahoogroups.com>
                    > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > <mailto:MentalCalculation%40yahoogroups.com>
                    > > > > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
                    > > <dacastro123@>
                    > > > > > wrote:
                    > > > > > > > > > >
                    > > > > > > > > > > Hi! I have a question for you...
                    > > > > > > > > > >
                    > > > > > > > > > > How can I calculate mentally high powers like, for example
                    > > > > 41^23?
                    > > > > > > > > > >
                    > > > > > > > > > > I read that it can be achivied using logs, but the result
                    > > will
                    > > > > not
                    > > > > > be accurate: log41 ~ 1,6128, so log 41^23 will be 37,0944. Doing
                    > 41^23
                    > > in
                    > > > > a
                    > > > > > calculator: =1,241734 x 10^37, but, with the use of antilog, I get
                    > > 1,24280
                    > > > > x
                    > > > > > 10^37. How can I find precisely every single digit of the power? How
                    > > many
                    > > > > > decimal places of logs will I need?
                    > > > > > > > > > >
                    > > > > > > > > > > And what about R�diger Gamm? Does he really have
                    > memorized
                    > > the
                    > > > > > powers? Does he use mnemonics?
                    > > > > > > > > > >
                    > > > > > > > > > > Thank You in advance
                    > > > > > > > > > >
                    > > > > > > > > >
                    > > > > > > > >
                    > > > > > > >
                    > > > > > >
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > >
                    > > > > > [Non-text portions of this message have been removed]
                    > > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > >
                    > > > > [Non-text portions of this message have been removed]
                    > > > >
                    > > >
                    > >
                    > >
                    > >
                    > >
                    > >
                    > > [Non-text portions of this message have been removed]
                    > >
                    >
                    >
                    >
                    >
                    >
                    > [Non-text portions of this message have been removed]
                    >
                  • A.W.A.P. Bouman
                    Good afternoon dear Daniel, To start with: I have no secrets about my calculation talent, and I do not want to tell fairy tales. In fact for me the essence of
                    Message 9 of 24 , Dec 10, 2012
                    • 0 Attachment
                      Good afternoon dear Daniel,



                      To start with: I have no secrets about my calculation talent, and I do not
                      want to tell fairy tales. In fact for me the essence of my talent is a great
                      mystery.

                      The literature I read about it all is not very helpful and instructive.
                      Pictures with green mand red fields in brain activity: what can we do with
                      this?

                      Another question: there has been done a lot of research on discalculi, i.e.
                      very low calcualtion abilities, I wonder if there has been a good research
                      about let us call it “supercalculi” the ability for very good mental
                      calculation.



                      As far as I know myself, I am a specific visual man. But I do not see
                      numbers in my head, I must for myself write down numbers, otherwise
                      everything is going wrong. I do remember that I wrote down the squares up to
                      1.000 in a calm way, not in a hurry. Binomial expansion is a mystery to me,
                      surely at the moment I was writing down the squares. I did nothing else but
                      writing the numbers and eg when I wrote 257² after 256² the addition was
                      made, so 65536 + 513= 66049. I cannot say whether 314×200+57² really speeds
                      up the calculation.



                      I am sorry not to be able to tell you more and useful things.





                      Kindest regards,





                      Willem Bouman











                      Van: MentalCalculation@yahoogroups.com
                      [mailto:MentalCalculation@yahoogroups.com] Namens dacastro93
                      Verzonden: maandag 10 december 2012 13:32
                      Aan: MentalCalculation@yahoogroups.com
                      Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
                      "trivial entertainment"





                      About your memory...do You hear the numbers or do You see them in your head?
                      How many times have You repeated the 1000 squares before getting them
                      stucked into your memory? I calculate them while walking with my dog and
                      repeat 2 to 3 times before memorizing, but I do review in the next day. To
                      calculate squares, what method is used? Binomial expansion? Because I'm
                      doing with the method I saw on Arthur Benjamin's book. For example 257^2, I
                      do 200x314 + 57^2. Is this the fastest method?

                      Thanks in advance,

                      Daniel

                      --- In MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
                      <awap.bouman@...> wrote:
                      >
                      > Hi Reto and fellow calculators,
                      >
                      >
                      >
                      > It is a pity, Reto, but you are right. And indeed getting confident with
                      the
                      > cubes develops along aonther path.
                      >
                      > But that does not mean that there is no structure in the cubes. The tens
                      > increase according to Newtons iteration.
                      >
                      > Let's start with 11. There the tens increase with 10 in comparison with 1.
                      > And the tens increase according to Newton as follows 3×1²×10, so with 30.
                      > And indeed 11³= 11 31, 21³ = 92 61
                      >
                      >
                      >
                      > 3³ = 27 and the trens of the cubes increase with 3×3²×10= 70. And look 13³
                      =
                      > 21 97, 23³ = 121 67. The best way to get confident is to calculate them
                      > yourself, rather than to take a stupid machine.
                      >
                      >
                      >
                      > Mnemonics: I read from other calculators that they associate numbers with:
                      > rooms in the house, pictures, you name it. I do
                      >
                      >
                      >
                      > it all without and have no idea how my memory works. I can only say that
                      the
                      > results are good. And are greatful fort hat.
                      >
                      >
                      >
                      > Kindest regards,
                      >
                      >
                      >
                      >
                      >
                      > Willem Bouman
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      > Van: MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > [mailto:MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com> ] Namens Retothejuggler
                      > Verzonden: donderdag 6 december 2012 13:59
                      > Aan: MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
                      > "trivial entertainment"
                      >
                      >
                      >
                      >
                      >
                      > Dear Willem
                      >
                      > How have you calculated the cubes? They can`t be broken down simply in a
                      row
                      > of additions (which you used to learn squares).
                      >
                      > It would be interesting to see your skills in memorizing numbers without
                      > mnemotechnic pictures.
                      >
                      > You`re doing this for years and are miles away from most, but I`ll choose
                      my
                      > numbers carefully :-).
                      >
                      > Pi is just for fun.
                      >
                      > Thanks for your input.
                      >
                      > Greetings Reto
                      >
                      > --- In MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
                      > <awap.bouman@> wrote:
                      > >
                      > > Dear fellow calculators,
                      > >
                      > >
                      > >
                      > > What should be in someones memory? At the moment I was aware of my
                      talent
                      > > memorising the squares up to 1.000 went more or less automatically. I
                      > > started with 1 and by addibng I came up to 1.000. My memory must be a
                      > > very good one: they are still there.
                      > >
                      > > In the same way the cubes up to 100.
                      > >
                      > > All the multiplications of 2 digit numbers were there from about my 9th
                      > > year.
                      > >
                      > >
                      > >
                      > > This is not very impressive, but with good algoritms one can do a lot
                      > more.
                      > >
                      > >
                      > >
                      > > I am not perfect in it, but can do – owing to the cross method which
                      > taught
                      > > me Wim Klein – multiplications of 8 digit numbers.
                      > >
                      > >
                      > >
                      > > Jan van Koningsveld and Robert Fountain taught me decimal roots, and
                      owing
                      > > tot hat knowledge I can do them , besides integer roots up to about 18
                      > > digits.
                      > >
                      > > Andy Robertshaw told interesting things about decimal cube roots.
                      > >
                      > >
                      > >
                      > > Having found the structure in the cubes I created an algortim and so can
                      > do
                      > > integer cube roots up to 24 digits.
                      > >
                      > >
                      > >
                      > > I have no idea what to do with x-decimals of pi.
                      > >
                      > > Last year I learnt the logaritms up to 100. They are gone because of
                      > > neglecting. But surely they are helpful in decimal roots, especially the
                      > > deep ones.
                      > >
                      > >
                      > >
                      > > For the younger ones amongst us I give the advise: consider which
                      > > possibilities there are in what you intend to do and then decide what
                      you
                      > > want to memorise.
                      > >
                      > >
                      > >
                      > > Memorising "blindly" a lot of numbers is not very creative, so think
                      very
                      > > well before beginning "a hell of a job".
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > > Kindest regards,
                      > >
                      > >
                      > >
                      > >
                      > >
                      > > Willem Bouman
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > > Van: MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com>
                      > > [mailto:MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com> ] Namens Retothejuggler
                      > > Verzonden: woensdag 5 december 2012 12:13
                      > > Aan: MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com>
                      > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
                      > > "trivial entertainment"
                      > >
                      > >
                      > >
                      > >
                      > >
                      > > I`m wondering what other numbers friends here have stored in their
                      minds,
                      > my
                      > > lame work is just 2-digit squares, 20 decimals of Pi, cubes up to 30 and
                      > > fith up to 12 right now and some primes...
                      > >
                      > > But I`m just back in it...there is hope...
                      > >
                      > > --- In MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com>
                      > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
                      > > <dacastro123@> wrote:
                      > > >
                      > > > That's why I like math! There's a reason for everything, there are
                      > > patterns everywhere..
                      > > >
                      > > > I'm 19 years old. Memorizing 1000 squares is very impressive! When I
                      was
                      > > 6, I memorized the first 20 powers of 2, but that's not really
                      > impressive...
                      > > >
                      > > > Cheers,
                      > > >
                      > > > Daniel
                      > > >
                      > > > --- In MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com>
                      > > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
                      > > <awap.bouman@> wrote:
                      > > > >
                      > > > > Dear Daniel,
                      > > > >
                      > > > >
                      > > > >
                      > > > > Well, I am a Dutchman, so neither native English speaker. But all
                      you
                      > > > > write, I understand. By the way: 38 and 62 end on 44, but also do 12
                      > and
                      > > 88.
                      > > > > The difference is in the hundreds. This concerns all the squares of
                      > the
                      > > even
                      > > > > numbers. See eg 08 and 92, squared 64 and 8464, EH ( even Hundreds)
                      > and
                      > > 42
                      > > > > and 58 squared resp. 1746 and 3364 OH (Odd Hundreds).
                      > > > >
                      > > > >
                      > > > >
                      > > > > In the squares of the odd numbers you'll see that the hundreds keep
                      > > their
                      > > > > nature. EG 13²=169, 37²=1369, 63²=3969, 87²=7569, all OH, odd
                      > hundreds.
                      > > > > Later on when you study the 3 digit squares, you'll see even
                      thousands
                      > > and
                      > > > > odd thousands.
                      > > > >
                      > > > > Eg 13²=169, ET ( Even Thousand), 237²=56169 (ET), 263²=69169,
                      > > 487²=237169,
                      > > > > both OT, 513²=263169 and 737²=543169, both OT, 763²=582169 and
                      > > > > 987²=974169, both ET.
                      > > > >
                      > > > > Besides you can see 13+987=1000, 237+763=1000 etc.
                      > > > >
                      > > > >
                      > > > >
                      > > > > All the best with your number studies and have fun wit hit!!!!!
                      > > > >
                      > > > >
                      > > > >
                      > > > > I do not know how old you are. Concerning myself: at 14 I knew all
                      the
                      > > > > squares up to 1000 and shortly after that all the cubes up to 100.
                      > With
                      > > that
                      > > > > I can do a lot of things.
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > > Kindest regards,
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > > Willem Bouman
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > > Van: MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com>
                      > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > [mailto:MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com>
                      > > <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
                      > > > > Verzonden: zondag 2 december 2012 1:39
                      > > > > Aan: MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com>
                      > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this
                      > under
                      > > > > "trivial entertainment"
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > > I'm sorry Mr. Bouman, my name is Daniel.
                      > > > >
                      > > > > These are nice properties! While memorizing the squares I observed
                      > that
                      > > > > numbers that add up to 100 have their squares with the same ending,
                      > for
                      > > > > example 38 and 62. Both add up to a hundred. 38 squared is 1444 and
                      62
                      > > > > squared is 3844, so the last to digits match.
                      > > > >
                      > > > > Mnemonic is anything that can help memorizing something. It might be
                      a
                      > > word,
                      > > > > a phrase or mental image that facilitate the process of memorizing.
                      > > > >
                      > > > > Well the squares are useful to me in multiplications, square roots
                      and
                      > > they
                      > > > > also help to square larger numbers. The other powers I would like to
                      > > > > memorize because I think it's fun :)
                      > > > >
                      > > > > Sorry if my english is bad. I'm from Brazil.
                      > > > >
                      > > > > Thank You
                      > > > >
                      > > > > --- In MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com>
                      > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
                      > > > > <awap.bouman@> wrote:
                      > > > > >
                      > > > > > Dear Mr. Dacastro93, or whom you may be,
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > > You could consider to subdivide the squares in groups with the
                      same
                      > > last
                      > > > > > digits, so from 1-100 you can do 1,49,51 and 99, all their squares
                      > end
                      > > on
                      > > > > > 01. Then you take 2,48,52 and 98, all their squares ending on 04.
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > > What I did as a school boy during the less interesting lessons, is
                      > > writing
                      > > > > > all the numbers 1 up to 1.000 on a list and calculated the squares
                      > by
                      > > > > > adding: 2² =1 + (2+1)=4, 3²= 4 +(2+3)=9.
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > > 670²=448900, 671²= 448900 + (670+671) = 450241.
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > > For the cubes: look after the structure. The tens increase
                      according
                      > > to-
                      > > > > if
                      > > > > > I am well informed - the iterationn of Newton.
                      > > > > >
                      > > > > > For 11 the increase of the tens is (3×1²×10) = 30 per ten, and
                      > indeed
                      > > 11³=
                      > > > > > 1331. For 21 the increase is 2×(3×1²×10) = 60, and indeed 21³ =
                      > 9261.
                      > > You
                      > > > > > have not everything, but there is a beginning.
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > > The following, still free of charge:
                      > > > > >
                      > > > > > 7³=343. IUncrease of the tens: 3×7²×10=70. Take 27³. Increase of
                      the
                      > > tens
                      > > > > > 2×70= 40. So the last digits of 27³ have to end on 83. And indeed
                      > 27³=
                      > > > > > 19683.
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > > As I have not the faintest idea of what mnmonics are, I cannot
                      help
                      > > you
                      > > > > with
                      > > > > > them.
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > > Did you consider what to do with the numbers you want to know by
                      > > heart?
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > > Kindest regards,
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > > Willem Bouman
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > > Van: MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com>
                      > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > > [mailto:MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com>
                      > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
                      > > > > > Verzonden: woensdag 28 november 2012 12:42
                      > > > > > Aan: MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com>
                      > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this
                      > > under
                      > > > > > "trivial entertainment"
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > > That was fun!
                      > > > > >
                      > > > > > The first 100 squares I memorized without the help of mnemonics.
                      How
                      > > long
                      > > > > > can I go without mnemonics? I think I might try the first 100
                      cubes
                      > by
                      > > > > rote
                      > > > > > memorization, just like I did with the squares..
                      > > > > >
                      > > > > > Cheers
                      > > > > >
                      > > > > > --- In MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com>
                      > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > > <mailto:MentalCalculation%40yahoogroups.com> , "Jerry"
                      <wholphin48@>
                      > > > > > wrote:
                      > > > > > >
                      > > > > > >
                      > > > > > > Here's a way to show the result of some great calculating with
                      no
                      > > > > work...
                      > > > > > >
                      > > > > > > Suppose a,b are positive integers, then you can write a^b in
                      base
                      > a
                      > > > > > precisely
                      > > > > > > as a 1 followed by b zeros...
                      > > > > > >
                      > > > > > > For example 6^8 in base six is 100000000 That doesn't mean you
                      > have
                      > > a
                      > > > > clue
                      > > > > > what that number is in base ten, the usual reference. But you have
                      > > > > expressed
                      > > > > > the result in base six precisely and instantly. However, this time
                      I
                      > > can
                      > > > > > tell you that 6^8 in base ten is equal to 1,679,616 :)
                      > > > > > >
                      > > > > > > Good luck with the mnemonics. I just thought this trivia might
                      > give
                      > > you
                      > > > > > all a humorous break!!
                      > > > > > >
                      > > > > > > Jerry Newport Tucson, AZ
                      > > > > > >
                      > > > > > > --- In MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com>
                      > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
                      > > <dacastro123@>
                      > > > > > wrote:
                      > > > > > > >
                      > > > > > > > Interesting! Like I said..I'll try to memorize the cubes of
                      > 1-100,
                      > > > > then
                      > > > > > I will come up with a mnemonic system in order to commit to memory
                      > > higher
                      > > > > > powers. Let's see what I can do.
                      > > > > > > >
                      > > > > > > > Cheers,
                      > > > > > > >
                      > > > > > > > Daniel
                      > > > > > > >
                      > > > > > > > --- In MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com>
                      > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > > <mailto:MentalCalculation%40yahoogroups.com> , "Retothejuggler"
                      > > > > > <retothejuggler@> wrote:
                      > > > > > > > >
                      > > > > > > > > In the last months, I quit mental calculation a bit and
                      > switched
                      > > > > over
                      > > > > > to sudoku and logical puzzle solving. A few weeks ago my numbers
                      > > hunger
                      > > > > came
                      > > > > > back and alongside this I found an older scientific article about
                      > > Rüdiger
                      > > > > > Gamm.
                      > > > > > > > >
                      > > > > > > > > Well, he learned the higher powers but still claims to
                      > construct
                      > > > > > powers out of known powers, no idea about how.
                      > > > > > > > >
                      > > > > > > > > If you want to know what can be calculated, history shows:
                      > > > > > > > >
                      > > > > > > > > Mlle Osaka, 2 digits up to the 10.th (probably from memory),
                      3
                      > > > > digits
                      > > > > > up to 8th.
                      > > > > > > > >
                      > > > > > > > > Oscar Verhaeghe 9 999 999 to the 5th., 40 seconds
                      > > > > > > > >
                      > > > > > > > > Marathe one digit up to the 20.th (probably from memory)
                      > > > > > > > >
                      > > > > > > > > Klein calculated a 16th.
                      > > > > > > > >
                      > > > > > > > > Any mnemonic armed and aarithemtic skilled person can do
                      > higher
                      > > ones
                      > > > > > but not in a matter of seconds.
                      > > > > > > > >
                      > > > > > > > > Thanks Ron again for our offline discussion.
                      > > > > > > > >
                      > > > > > > > >
                      > > > > > > > >
                      > > > > > > > > --- In MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com>
                      > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > > <mailto:MentalCalculation%40yahoogroups.com> , "rondrond1"
                      > <doerfpub@>
                      > > > > > wrote:
                      > > > > > > > > >
                      > > > > > > > > > That's a very good question. Reto and I have discussed
                      this
                      > > > > offline
                      > > > > > in the past, and we did not come up with a good solution for high
                      > > powers.
                      > > > > I
                      > > > > > believe the number of significant digits of the logarithm would
                      have
                      > > to
                      > > > > > equal the number of significant digits of the solution, although
                      the
                      > > last
                      > > > > > few digits of the answer might be found from the last few digits
                      of
                      > > the
                      > > > > > problem and also two of the digits can be found from 99-remainder
                      > (mod
                      > > 99)
                      > > > > > calculations if the rest of the digits are known. R�diger Gamm
                      > would
                      > > > > > probably have memorized high powers, although I can't definitively
                      > say
                      > > > > that
                      > > > > > since I don't know the method or methods he uses.
                      > > > > > > > > >
                      > > > > > > > > > Ron
                      > > > > > > > > >
                      > > > > > > > > > --- In MentalCalculation@yahoogroups.com
                      <mailto:MentalCalculation%40yahoogroups.com>
                      > <mailto:MentalCalculation%40yahoogroups.com>
                      > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > <mailto:MentalCalculation%40yahoogroups.com>
                      > > > > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
                      > > <dacastro123@>
                      > > > > > wrote:
                      > > > > > > > > > >
                      > > > > > > > > > > Hi! I have a question for you...
                      > > > > > > > > > >
                      > > > > > > > > > > How can I calculate mentally high powers like, for
                      example
                      > > > > 41^23?
                      > > > > > > > > > >
                      > > > > > > > > > > I read that it can be achivied using logs, but the
                      result
                      > > will
                      > > > > not
                      > > > > > be accurate: log41 ~ 1,6128, so log 41^23 will be 37,0944. Doing
                      > 41^23
                      > > in
                      > > > > a
                      > > > > > calculator: =1,241734 x 10^37, but, with the use of antilog, I get
                      > > 1,24280
                      > > > > x
                      > > > > > 10^37. How can I find precisely every single digit of the power?
                      How
                      > > many
                      > > > > > decimal places of logs will I need?
                      > > > > > > > > > >
                      > > > > > > > > > > And what about R�diger Gamm? Does he really have
                      > memorized
                      > > the
                      > > > > > powers? Does he use mnemonics?
                      > > > > > > > > > >
                      > > > > > > > > > > Thank You in advance
                      > > > > > > > > > >
                      > > > > > > > > >
                      > > > > > > > >
                      > > > > > > >
                      > > > > > >
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > >
                      > > > > > [Non-text portions of this message have been removed]
                      > > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > >
                      > > > > [Non-text portions of this message have been removed]
                      > > > >
                      > > >
                      > >
                      > >
                      > >
                      > >
                      > >
                      > > [Non-text portions of this message have been removed]
                      > >
                      >
                      >
                      >
                      >
                      >
                      > [Non-text portions of this message have been removed]
                      >





                      [Non-text portions of this message have been removed]
                    • dacastro93
                      Things will be really interesting if someone do a deep research on mental calculation...to explain what is happening in the brain while calculating, just like
                      Message 10 of 24 , Dec 11, 2012
                      • 0 Attachment
                        Things will be really interesting if someone do a deep research on mental calculation...to explain what is happening in the brain while calculating, just like that study about Ruediger Gamm, but with more people involved. They could take the best calculators, than above average calculators who are training, and the worst calculators, to see what's the difference between their brains.

                        Cheers,

                        Daniel

                        --- In MentalCalculation@yahoogroups.com, "A.W.A.P. Bouman" <awap.bouman@...> wrote:
                        >
                        > Good afternoon dear Daniel,
                        >
                        >
                        >
                        > To start with: I have no secrets about my calculation talent, and I do not
                        > want to tell fairy tales. In fact for me the essence of my talent is a great
                        > mystery.
                        >
                        > The literature I read about it all is not very helpful and instructive.
                        > Pictures with green mand red fields in brain activity: what can we do with
                        > this?
                        >
                        > Another question: there has been done a lot of research on discalculi, i.e.
                        > very low calcualtion abilities, I wonder if there has been a good research
                        > about let us call it "supercalculi" the ability for very good mental
                        > calculation.
                        >
                        >
                        >
                        > As far as I know myself, I am a specific visual man. But I do not see
                        > numbers in my head, I must for myself write down numbers, otherwise
                        > everything is going wrong. I do remember that I wrote down the squares up to
                        > 1.000 in a calm way, not in a hurry. Binomial expansion is a mystery to me,
                        > surely at the moment I was writing down the squares. I did nothing else but
                        > writing the numbers and eg when I wrote 257² after 256² the addition was
                        > made, so 65536 + 513= 66049. I cannot say whether 314×200+57² really speeds
                        > up the calculation.
                        >
                        >
                        >
                        > I am sorry not to be able to tell you more and useful things.
                        >
                        >
                        >
                        >
                        >
                        > Kindest regards,
                        >
                        >
                        >
                        >
                        >
                        > Willem Bouman
                        >
                        >
                        >
                        >
                        >
                        >
                        >
                        >
                        >
                        >
                        >
                        > Van: MentalCalculation@yahoogroups.com
                        > [mailto:MentalCalculation@yahoogroups.com] Namens dacastro93
                        > Verzonden: maandag 10 december 2012 13:32
                        > Aan: MentalCalculation@yahoogroups.com
                        > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
                        > "trivial entertainment"
                        >
                        >
                        >
                        >
                        >
                        > About your memory...do You hear the numbers or do You see them in your head?
                        > How many times have You repeated the 1000 squares before getting them
                        > stucked into your memory? I calculate them while walking with my dog and
                        > repeat 2 to 3 times before memorizing, but I do review in the next day. To
                        > calculate squares, what method is used? Binomial expansion? Because I'm
                        > doing with the method I saw on Arthur Benjamin's book. For example 257^2, I
                        > do 200x314 + 57^2. Is this the fastest method?
                        >
                        > Thanks in advance,
                        >
                        > Daniel
                        >
                        > --- In MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
                        > <awap.bouman@> wrote:
                        > >
                        > > Hi Reto and fellow calculators,
                        > >
                        > >
                        > >
                        > > It is a pity, Reto, but you are right. And indeed getting confident with
                        > the
                        > > cubes develops along aonther path.
                        > >
                        > > But that does not mean that there is no structure in the cubes. The tens
                        > > increase according to Newtons iteration.
                        > >
                        > > Let's start with 11. There the tens increase with 10 in comparison with 1.
                        > > And the tens increase according to Newton as follows 3×1²×10, so with 30.
                        > > And indeed 11³= 11 31, 21³ = 92 61
                        > >
                        > >
                        > >
                        > > 3³ = 27 and the trens of the cubes increase with 3×3²×10= 70. And look 13³
                        > =
                        > > 21 97, 23³ = 121 67. The best way to get confident is to calculate them
                        > > yourself, rather than to take a stupid machine.
                        > >
                        > >
                        > >
                        > > Mnemonics: I read from other calculators that they associate numbers with:
                        > > rooms in the house, pictures, you name it. I do
                        > >
                        > >
                        > >
                        > > it all without and have no idea how my memory works. I can only say that
                        > the
                        > > results are good. And are greatful fort hat.
                        > >
                        > >
                        > >
                        > > Kindest regards,
                        > >
                        > >
                        > >
                        > >
                        > >
                        > > Willem Bouman
                        > >
                        > >
                        > >
                        > >
                        > >
                        > >
                        > >
                        > >
                        > >
                        > >
                        > >
                        > >
                        > >
                        > >
                        > >
                        > >
                        > >
                        > > Van: MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > [mailto:MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com> ] Namens Retothejuggler
                        > > Verzonden: donderdag 6 december 2012 13:59
                        > > Aan: MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
                        > > "trivial entertainment"
                        > >
                        > >
                        > >
                        > >
                        > >
                        > > Dear Willem
                        > >
                        > > How have you calculated the cubes? They can`t be broken down simply in a
                        > row
                        > > of additions (which you used to learn squares).
                        > >
                        > > It would be interesting to see your skills in memorizing numbers without
                        > > mnemotechnic pictures.
                        > >
                        > > You`re doing this for years and are miles away from most, but I`ll choose
                        > my
                        > > numbers carefully :-).
                        > >
                        > > Pi is just for fun.
                        > >
                        > > Thanks for your input.
                        > >
                        > > Greetings Reto
                        > >
                        > > --- In MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
                        > > <awap.bouman@> wrote:
                        > > >
                        > > > Dear fellow calculators,
                        > > >
                        > > >
                        > > >
                        > > > What should be in someones memory? At the moment I was aware of my
                        > talent
                        > > > memorising the squares up to 1.000 went more or less automatically. I
                        > > > started with 1 and by addibng I came up to 1.000. My memory must be a
                        > > > very good one: they are still there.
                        > > >
                        > > > In the same way the cubes up to 100.
                        > > >
                        > > > All the multiplications of 2 digit numbers were there from about my 9th
                        > > > year.
                        > > >
                        > > >
                        > > >
                        > > > This is not very impressive, but with good algoritms one can do a lot
                        > > more.
                        > > >
                        > > >
                        > > >
                        > > > I am not perfect in it, but can do – owing to the cross method which
                        > > taught
                        > > > me Wim Klein – multiplications of 8 digit numbers.
                        > > >
                        > > >
                        > > >
                        > > > Jan van Koningsveld and Robert Fountain taught me decimal roots, and
                        > owing
                        > > > tot hat knowledge I can do them , besides integer roots up to about 18
                        > > > digits.
                        > > >
                        > > > Andy Robertshaw told interesting things about decimal cube roots.
                        > > >
                        > > >
                        > > >
                        > > > Having found the structure in the cubes I created an algortim and so can
                        > > do
                        > > > integer cube roots up to 24 digits.
                        > > >
                        > > >
                        > > >
                        > > > I have no idea what to do with x-decimals of pi.
                        > > >
                        > > > Last year I learnt the logaritms up to 100. They are gone because of
                        > > > neglecting. But surely they are helpful in decimal roots, especially the
                        > > > deep ones.
                        > > >
                        > > >
                        > > >
                        > > > For the younger ones amongst us I give the advise: consider which
                        > > > possibilities there are in what you intend to do and then decide what
                        > you
                        > > > want to memorise.
                        > > >
                        > > >
                        > > >
                        > > > Memorising "blindly" a lot of numbers is not very creative, so think
                        > very
                        > > > well before beginning "a hell of a job".
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > > Kindest regards,
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > > Willem Bouman
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > > Van: MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > [mailto:MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com> ] Namens Retothejuggler
                        > > > Verzonden: woensdag 5 december 2012 12:13
                        > > > Aan: MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this under
                        > > > "trivial entertainment"
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > > I`m wondering what other numbers friends here have stored in their
                        > minds,
                        > > my
                        > > > lame work is just 2-digit squares, 20 decimals of Pi, cubes up to 30 and
                        > > > fith up to 12 right now and some primes...
                        > > >
                        > > > But I`m just back in it...there is hope...
                        > > >
                        > > > --- In MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
                        > > > <dacastro123@> wrote:
                        > > > >
                        > > > > That's why I like math! There's a reason for everything, there are
                        > > > patterns everywhere..
                        > > > >
                        > > > > I'm 19 years old. Memorizing 1000 squares is very impressive! When I
                        > was
                        > > > 6, I memorized the first 20 powers of 2, but that's not really
                        > > impressive...
                        > > > >
                        > > > > Cheers,
                        > > > >
                        > > > > Daniel
                        > > > >
                        > > > > --- In MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
                        > > > <awap.bouman@> wrote:
                        > > > > >
                        > > > > > Dear Daniel,
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > > Well, I am a Dutchman, so neither native English speaker. But all
                        > you
                        > > > > > write, I understand. By the way: 38 and 62 end on 44, but also do 12
                        > > and
                        > > > 88.
                        > > > > > The difference is in the hundreds. This concerns all the squares of
                        > > the
                        > > > even
                        > > > > > numbers. See eg 08 and 92, squared 64 and 8464, EH ( even Hundreds)
                        > > and
                        > > > 42
                        > > > > > and 58 squared resp. 1746 and 3364 OH (Odd Hundreds).
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > > In the squares of the odd numbers you'll see that the hundreds keep
                        > > > their
                        > > > > > nature. EG 13²=169, 37²=1369, 63²=3969, 87²=7569, all OH, odd
                        > > hundreds.
                        > > > > > Later on when you study the 3 digit squares, you'll see even
                        > thousands
                        > > > and
                        > > > > > odd thousands.
                        > > > > >
                        > > > > > Eg 13²=169, ET ( Even Thousand), 237²=56169 (ET), 263²=69169,
                        > > > 487²=237169,
                        > > > > > both OT, 513²=263169 and 737²=543169, both OT, 763²=582169 and
                        > > > > > 987²=974169, both ET.
                        > > > > >
                        > > > > > Besides you can see 13+987=1000, 237+763=1000 etc.
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > > All the best with your number studies and have fun wit hit!!!!!
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > > I do not know how old you are. Concerning myself: at 14 I knew all
                        > the
                        > > > > > squares up to 1000 and shortly after that all the cubes up to 100.
                        > > With
                        > > > that
                        > > > > > I can do a lot of things.
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > > Kindest regards,
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > > Willem Bouman
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > > Van: MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > [mailto:MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
                        > > > > > Verzonden: zondag 2 december 2012 1:39
                        > > > > > Aan: MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this
                        > > under
                        > > > > > "trivial entertainment"
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > > I'm sorry Mr. Bouman, my name is Daniel.
                        > > > > >
                        > > > > > These are nice properties! While memorizing the squares I observed
                        > > that
                        > > > > > numbers that add up to 100 have their squares with the same ending,
                        > > for
                        > > > > > example 38 and 62. Both add up to a hundred. 38 squared is 1444 and
                        > 62
                        > > > > > squared is 3844, so the last to digits match.
                        > > > > >
                        > > > > > Mnemonic is anything that can help memorizing something. It might be
                        > a
                        > > > word,
                        > > > > > a phrase or mental image that facilitate the process of memorizing.
                        > > > > >
                        > > > > > Well the squares are useful to me in multiplications, square roots
                        > and
                        > > > they
                        > > > > > also help to square larger numbers. The other powers I would like to
                        > > > > > memorize because I think it's fun :)
                        > > > > >
                        > > > > > Sorry if my english is bad. I'm from Brazil.
                        > > > > >
                        > > > > > Thank You
                        > > > > >
                        > > > > > --- In MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman"
                        > > > > > <awap.bouman@> wrote:
                        > > > > > >
                        > > > > > > Dear Mr. Dacastro93, or whom you may be,
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > > You could consider to subdivide the squares in groups with the
                        > same
                        > > > last
                        > > > > > > digits, so from 1-100 you can do 1,49,51 and 99, all their squares
                        > > end
                        > > > on
                        > > > > > > 01. Then you take 2,48,52 and 98, all their squares ending on 04.
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > > What I did as a school boy during the less interesting lessons, is
                        > > > writing
                        > > > > > > all the numbers 1 up to 1.000 on a list and calculated the squares
                        > > by
                        > > > > > > adding: 2² =1 + (2+1)=4, 3²= 4 +(2+3)=9.
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > > 670²=448900, 671²= 448900 + (670+671) = 450241.
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > > For the cubes: look after the structure. The tens increase
                        > according
                        > > > to-
                        > > > > > if
                        > > > > > > I am well informed - the iterationn of Newton.
                        > > > > > >
                        > > > > > > For 11 the increase of the tens is (3×1²×10) = 30 per ten, and
                        > > indeed
                        > > > 11³=
                        > > > > > > 1331. For 21 the increase is 2×(3×1²×10) = 60, and indeed 21³ =
                        > > 9261.
                        > > > You
                        > > > > > > have not everything, but there is a beginning.
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > > The following, still free of charge:
                        > > > > > >
                        > > > > > > 7³=343. IUncrease of the tens: 3×7²×10=70. Take 27³. Increase of
                        > the
                        > > > tens
                        > > > > > > 2×70= 40. So the last digits of 27³ have to end on 83. And indeed
                        > > 27³=
                        > > > > > > 19683.
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > > As I have not the faintest idea of what mnmonics are, I cannot
                        > help
                        > > > you
                        > > > > > with
                        > > > > > > them.
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > > Did you consider what to do with the numbers you want to know by
                        > > > heart?
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > > Kindest regards,
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > > Willem Bouman
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > > Van: MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > > [mailto:MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
                        > > > > > > Verzonden: woensdag 28 november 2012 12:42
                        > > > > > > Aan: MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > > Onderwerp: [Mental Calculation] Re: Calculating Powers, file this
                        > > > under
                        > > > > > > "trivial entertainment"
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > > That was fun!
                        > > > > > >
                        > > > > > > The first 100 squares I memorized without the help of mnemonics.
                        > How
                        > > > long
                        > > > > > > can I go without mnemonics? I think I might try the first 100
                        > cubes
                        > > by
                        > > > > > rote
                        > > > > > > memorization, just like I did with the squares..
                        > > > > > >
                        > > > > > > Cheers
                        > > > > > >
                        > > > > > > --- In MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > > <mailto:MentalCalculation%40yahoogroups.com> , "Jerry"
                        > <wholphin48@>
                        > > > > > > wrote:
                        > > > > > > >
                        > > > > > > >
                        > > > > > > > Here's a way to show the result of some great calculating with
                        > no
                        > > > > > work...
                        > > > > > > >
                        > > > > > > > Suppose a,b are positive integers, then you can write a^b in
                        > base
                        > > a
                        > > > > > > precisely
                        > > > > > > > as a 1 followed by b zeros...
                        > > > > > > >
                        > > > > > > > For example 6^8 in base six is 100000000 That doesn't mean you
                        > > have
                        > > > a
                        > > > > > clue
                        > > > > > > what that number is in base ten, the usual reference. But you have
                        > > > > > expressed
                        > > > > > > the result in base six precisely and instantly. However, this time
                        > I
                        > > > can
                        > > > > > > tell you that 6^8 in base ten is equal to 1,679,616 :)
                        > > > > > > >
                        > > > > > > > Good luck with the mnemonics. I just thought this trivia might
                        > > give
                        > > > you
                        > > > > > > all a humorous break!!
                        > > > > > > >
                        > > > > > > > Jerry Newport Tucson, AZ
                        > > > > > > >
                        > > > > > > > --- In MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
                        > > > <dacastro123@>
                        > > > > > > wrote:
                        > > > > > > > >
                        > > > > > > > > Interesting! Like I said..I'll try to memorize the cubes of
                        > > 1-100,
                        > > > > > then
                        > > > > > > I will come up with a mnemonic system in order to commit to memory
                        > > > higher
                        > > > > > > powers. Let's see what I can do.
                        > > > > > > > >
                        > > > > > > > > Cheers,
                        > > > > > > > >
                        > > > > > > > > Daniel
                        > > > > > > > >
                        > > > > > > > > --- In MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > > <mailto:MentalCalculation%40yahoogroups.com> , "Retothejuggler"
                        > > > > > > <retothejuggler@> wrote:
                        > > > > > > > > >
                        > > > > > > > > > In the last months, I quit mental calculation a bit and
                        > > switched
                        > > > > > over
                        > > > > > > to sudoku and logical puzzle solving. A few weeks ago my numbers
                        > > > hunger
                        > > > > > came
                        > > > > > > back and alongside this I found an older scientific article about
                        > > > Rüdiger
                        > > > > > > Gamm.
                        > > > > > > > > >
                        > > > > > > > > > Well, he learned the higher powers but still claims to
                        > > construct
                        > > > > > > powers out of known powers, no idea about how.
                        > > > > > > > > >
                        > > > > > > > > > If you want to know what can be calculated, history shows:
                        > > > > > > > > >
                        > > > > > > > > > Mlle Osaka, 2 digits up to the 10.th (probably from memory),
                        > 3
                        > > > > > digits
                        > > > > > > up to 8th.
                        > > > > > > > > >
                        > > > > > > > > > Oscar Verhaeghe 9 999 999 to the 5th., 40 seconds
                        > > > > > > > > >
                        > > > > > > > > > Marathe one digit up to the 20.th (probably from memory)
                        > > > > > > > > >
                        > > > > > > > > > Klein calculated a 16th.
                        > > > > > > > > >
                        > > > > > > > > > Any mnemonic armed and aarithemtic skilled person can do
                        > > higher
                        > > > ones
                        > > > > > > but not in a matter of seconds.
                        > > > > > > > > >
                        > > > > > > > > > Thanks Ron again for our offline discussion.
                        > > > > > > > > >
                        > > > > > > > > >
                        > > > > > > > > >
                        > > > > > > > > > --- In MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > > <mailto:MentalCalculation%40yahoogroups.com> , "rondrond1"
                        > > <doerfpub@>
                        > > > > > > wrote:
                        > > > > > > > > > >
                        > > > > > > > > > > That's a very good question. Reto and I have discussed
                        > this
                        > > > > > offline
                        > > > > > > in the past, and we did not come up with a good solution for high
                        > > > powers.
                        > > > > > I
                        > > > > > > believe the number of significant digits of the logarithm would
                        > have
                        > > > to
                        > > > > > > equal the number of significant digits of the solution, although
                        > the
                        > > > last
                        > > > > > > few digits of the answer might be found from the last few digits
                        > of
                        > > > the
                        > > > > > > problem and also two of the digits can be found from 99-remainder
                        > > (mod
                        > > > 99)
                        > > > > > > calculations if the rest of the digits are known. R�diger Gamm
                        > > would
                        > > > > > > probably have memorized high powers, although I can't definitively
                        > > say
                        > > > > > that
                        > > > > > > since I don't know the method or methods he uses.
                        > > > > > > > > > >
                        > > > > > > > > > > Ron
                        > > > > > > > > > >
                        > > > > > > > > > > --- In MentalCalculation@yahoogroups.com
                        > <mailto:MentalCalculation%40yahoogroups.com>
                        > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > <mailto:MentalCalculation%40yahoogroups.com>
                        > > > > > > <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93"
                        > > > <dacastro123@>
                        > > > > > > wrote:
                        > > > > > > > > > > >
                        > > > > > > > > > > > Hi! I have a question for you...
                        > > > > > > > > > > >
                        > > > > > > > > > > > How can I calculate mentally high powers like, for
                        > example
                        > > > > > 41^23?
                        > > > > > > > > > > >
                        > > > > > > > > > > > I read that it can be achivied using logs, but the
                        > result
                        > > > will
                        > > > > > not
                        > > > > > > be accurate: log41 ~ 1,6128, so log 41^23 will be 37,0944. Doing
                        > > 41^23
                        > > > in
                        > > > > > a
                        > > > > > > calculator: =1,241734 x 10^37, but, with the use of antilog, I get
                        > > > 1,24280
                        > > > > > x
                        > > > > > > 10^37. How can I find precisely every single digit of the power?
                        > How
                        > > > many
                        > > > > > > decimal places of logs will I need?
                        > > > > > > > > > > >
                        > > > > > > > > > > > And what about R�diger Gamm? Does he really have
                        > > memorized
                        > > > the
                        > > > > > > powers? Does he use mnemonics?
                        > > > > > > > > > > >
                        > > > > > > > > > > > Thank You in advance
                        > > > > > > > > > > >
                        > > > > > > > > > >
                        > > > > > > > > >
                        > > > > > > > >
                        > > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > >
                        > > > > > > [Non-text portions of this message have been removed]
                        > > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > >
                        > > > > > [Non-text portions of this message have been removed]
                        > > > > >
                        > > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > >
                        > > > [Non-text portions of this message have been removed]
                        > > >
                        > >
                        > >
                        > >
                        > >
                        > >
                        > > [Non-text portions of this message have been removed]
                        > >
                        >
                        >
                        >
                        >
                        >
                        > [Non-text portions of this message have been removed]
                        >
                      • rondrond1
                        And yet, although Rudiger Gamm s brain scans are analyzed and published as the areas of the brain involved in mental calculation, isn t it more likely in his
                        Message 11 of 24 , Dec 11, 2012
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                          And yet, although Rudiger Gamm's brain scans are analyzed and published as the areas of the brain involved in mental calculation, isn't it more likely in his case that they are the areas of the brain involved in deep memory recall?? It seems to me that this basic misunderstanding makes the science as flawed as most other studies of mental calculators.

                          Ron

                          --- In MentalCalculation@yahoogroups.com, "dacastro93" <dacastro123@...> wrote:
                          >
                          > Things will be really interesting if someone do a deep research on mental calculation...to explain what is happening in the brain while calculating, just like that study about Ruediger Gamm, but with more people involved. They could take the best calculators, than above average calculators who are training, and the worst calculators, to see what's the difference between their brains.
                          >
                          > Cheers,
                          >
                          > Daniel
                        • Retothejuggler
                          In a study it says: For example, knowing perfectly squares and cubes, he started to grasp the relationships between powers and used this memorised knowledge
                          Message 12 of 24 , Dec 12, 2012
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                            In a study it says:

                            "For example, knowing perfectly squares and cubes, he started to grasp the relationships between powers and used this memorised knowledge to learn how to raise numbers to new powers."

                            For me, this is not really helpful because a power is a chain of multiplications and will always be...:-).










                            --- In MentalCalculation@yahoogroups.com, "rondrond1" <doerfpub@...> wrote:
                            >
                            >
                            >
                            > And yet, although Rudiger Gamm's brain scans are analyzed and published as the areas of the brain involved in mental calculation, isn't it more likely in his case that they are the areas of the brain involved in deep memory recall?? It seems to me that this basic misunderstanding makes the science as flawed as most other studies of mental calculators.
                            >
                            > Ron
                            >
                            > --- In MentalCalculation@yahoogroups.com, "dacastro93" <dacastro123@> wrote:
                            > >
                            > > Things will be really interesting if someone do a deep research on mental calculation...to explain what is happening in the brain while calculating, just like that study about Ruediger Gamm, but with more people involved. They could take the best calculators, than above average calculators who are training, and the worst calculators, to see what's the difference between their brains.
                            > >
                            > > Cheers,
                            > >
                            > > Daniel
                            >
                          • Retothejuggler
                            Hello, have you since ever used the dominic? I`m currently learning a major system (just up to 100) and have learned that R�diger Gamm either has 300`000 loci
                            Message 13 of 24 , Jan 20, 2013
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                              Hello, have you since ever used the dominic? I`m currently learning a major system (just up to 100) and have learned that Rüdiger Gamm either has 300`000 loci points or another system to memorize this mass of numbers accurately.


                              --- In MentalCalculation@yahoogroups.com, "dacastro93" wrote:
                              >
                              > Hi Ron! I'm aware of this mnemonic system, but I was thinking about using the Dominic System. I actually have already 91 numbers covered, it's just missing 9 person-actions.
                              >
                              > Thanks
                              >
                              > --- In MentalCalculation@yahoogroups.com, "rondrond1" wrote:
                              > >
                              > >
                              > >
                              > >
                              > > Hi Daniel,
                              > >
                              > > I don't know if you'll find this helpful or not:
                              > >
                              > > http://www.myreckonings.com/Dead_Reckoning/Online/Materials/Mnemonics_for_Squares_and_Cubes.pdf
                              > >
                              > > It's one of my set of online materials related to my book. The papers can be found at
                              > >
                              > > http://www.myreckonings.com/Dead_Reckoning/Online/Online_Material.htm
                              > >
                              > > Reto, I wish we had been able to come up with something useful for high powers. You had good ideas but I wasn't able to help much in the end.
                              > >
                              > > Cheers,
                              > >
                              > > Ron
                              > >
                              > >
                              > > --- In MentalCalculation@yahoogroups.com, "dacastro93" wrote:
                              > > >
                              > > > Interesting! Like I said..I'll try to memorize the cubes of 1-100, then I will come up with a mnemonic system in order to commit to memory higher powers. Let's see what I can do.
                              > > >
                              > > > Cheers,
                              > > >
                              > > > Daniel
                              > > >
                              > > > --- In MentalCalculation@yahoogroups.com, "Retothejuggler" wrote:
                              > > > >
                              > > > > In the last months, I quit mental calculation a bit and switched over to sudoku and logical puzzle solving. A few weeks ago my numbers hunger came back and alongside this I found an older scientific article about Rüdiger Gamm.
                              > > > >
                              > > > > Well, he learned the higher powers but still claims to construct powers out of known powers, no idea about how.
                              > > > >
                              > > > > If you want to know what can be calculated, history shows:
                              > > > >
                              > > > > Mlle Osaka, 2 digits up to the 10.th (probably from memory), 3 digits up to 8th.
                              > > > >
                              > > > > Oscar Verhaeghe 9 999 999 to the 5th., 40 seconds
                              > > > >
                              > > > > Marathe one digit up to the 20.th (probably from memory)
                              > > > >
                              > > > > Klein calculated a 16th.
                              > > > >
                              > > > > Any mnemonic armed and aarithemtic skilled person can do higher ones but not in a matter of seconds.
                              > > > >
                              > > > > Thanks Ron again for our offline discussion.
                              > > > >
                              > > > >
                              > > > >
                              > > > > --- In MentalCalculation@yahoogroups.com, "rondrond1" wrote:
                              > > > > >
                              > > > > > That's a very good question. Reto and I have discussed this offline in the past, and we did not come up with a good solution for high powers. I believe the number of significant digits of the logarithm would have to equal the number of significant digits of the solution, although the last few digits of the answer might be found from the last few digits of the problem and also two of the digits can be found from 99-remainder (mod 99) calculations if the rest of the digits are known. R�diger Gamm would probably have memorized high powers, although I can't definitively say that since I don't know the method or methods he uses.
                              > > > > >
                              > > > > > Ron
                              > > > > >
                              > > > > > --- In MentalCalculation@yahoogroups.com, "dacastro93" wrote:
                              > > > > > >
                              > > > > > > Hi! I have a question for you...
                              > > > > > >
                              > > > > > > How can I calculate mentally high powers like, for example 41^23?
                              > > > > > >
                              > > > > > > I read that it can be achivied using logs, but the result will not be accurate: log41 ~ 1,6128, so log 41^23 will be 37,0944. Doing 41^23 in a calculator: =1,241734 x 10^37, but, with the use of antilog, I get 1,24280 x 10^37. How can I find precisely every single digit of the power? How many decimal places of logs will I need?
                              > > > > > >
                              > > > > > > And what about R�diger Gamm? Does he really have memorized the powers? Does he use mnemonics?
                              > > > > > >
                              > > > > > > Thank You in advance
                              > > > > > >
                              > > > > >
                              > > > >
                              > > >
                              > >
                              >
                            • dacastro93
                              Hi! I have used the Major System, and it s really good, but with the Dominic System I can put 4 digits per locus, which is an advantage if You want to work
                              Message 14 of 24 , Jan 21, 2013
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                                Hi! I have used the Major System, and it's really good, but with the Dominic System I can put 4 digits per locus, which is an advantage if You want to work with big numbers as our case (I supose). The problem with the Dominic System, in my opinion, is the difficulty to find 100 people and 100 actions. I'm missing 6 person/actions. The Major System, on the other hand, was much easier to build.

                                As for Gamm, i read somewhere in this forum that He doesn't uses mnemonics, but I'm not sure. He says everybody can do what He does with proper training. Well, I have memorized the first 100 digits of Pi, the first 100 squares, the first 20 cubes and some logs without mnemonics. But I don't know how far it is possible to go without any technique. If He memorized 100^100 with mnemonics, He probably would need a journey for each number. I guess we will only know if He answers.

                                Cheers,

                                Daniel

                                --- In MentalCalculation@yahoogroups.com, "Retothejuggler" wrote:
                                >
                                > Hello, have you since ever used the dominic? I`m currently learning a major system (just up to 100) and have learned that Rüdiger Gamm either has 300`000 loci points or another system to memorize this mass of numbers accurately.
                                >
                                >
                                > --- In MentalCalculation@yahoogroups.com, "dacastro93" wrote:
                                > >
                                > > Hi Ron! I'm aware of this mnemonic system, but I was thinking about using the Dominic System. I actually have already 91 numbers covered, it's just missing 9 person-actions.
                                > >
                                > > Thanks
                                > >
                                > > --- In MentalCalculation@yahoogroups.com, "rondrond1" wrote:
                                > > >
                                > > >
                                > > >
                                > > >
                                > > > Hi Daniel,
                                > > >
                                > > > I don't know if you'll find this helpful or not:
                                > > >
                                > > > http://www.myreckonings.com/Dead_Reckoning/Online/Materials/Mnemonics_for_Squares_and_Cubes.pdf
                                > > >
                                > > > It's one of my set of online materials related to my book. The papers can be found at
                                > > >
                                > > > http://www.myreckonings.com/Dead_Reckoning/Online/Online_Material.htm
                                > > >
                                > > > Reto, I wish we had been able to come up with something useful for high powers. You had good ideas but I wasn't able to help much in the end.
                                > > >
                                > > > Cheers,
                                > > >
                                > > > Ron
                                > > >
                                > > >
                                > > > --- In MentalCalculation@yahoogroups.com, "dacastro93" wrote:
                                > > > >
                                > > > > Interesting! Like I said..I'll try to memorize the cubes of 1-100, then I will come up with a mnemonic system in order to commit to memory higher powers. Let's see what I can do.
                                > > > >
                                > > > > Cheers,
                                > > > >
                                > > > > Daniel
                                > > > >
                                > > > > --- In MentalCalculation@yahoogroups.com, "Retothejuggler" wrote:
                                > > > > >
                                > > > > > In the last months, I quit mental calculation a bit and switched over to sudoku and logical puzzle solving. A few weeks ago my numbers hunger came back and alongside this I found an older scientific article about Rüdiger Gamm.
                                > > > > >
                                > > > > > Well, he learned the higher powers but still claims to construct powers out of known powers, no idea about how.
                                > > > > >
                                > > > > > If you want to know what can be calculated, history shows:
                                > > > > >
                                > > > > > Mlle Osaka, 2 digits up to the 10.th (probably from memory), 3 digits up to 8th.
                                > > > > >
                                > > > > > Oscar Verhaeghe 9 999 999 to the 5th., 40 seconds
                                > > > > >
                                > > > > > Marathe one digit up to the 20.th (probably from memory)
                                > > > > >
                                > > > > > Klein calculated a 16th.
                                > > > > >
                                > > > > > Any mnemonic armed and aarithemtic skilled person can do higher ones but not in a matter of seconds.
                                > > > > >
                                > > > > > Thanks Ron again for our offline discussion.
                                > > > > >
                                > > > > >
                                > > > > >
                                > > > > > --- In MentalCalculation@yahoogroups.com, "rondrond1" wrote:
                                > > > > > >
                                > > > > > > That's a very good question. Reto and I have discussed this offline in the past, and we did not come up with a good solution for high powers. I believe the number of significant digits of the logarithm would have to equal the number of significant digits of the solution, although the last few digits of the answer might be found from the last few digits of the problem and also two of the digits can be found from 99-remainder (mod 99) calculations if the rest of the digits are known. R�diger Gamm would probably have memorized high powers, although I can't definitively say that since I don't know the method or methods he uses.
                                > > > > > >
                                > > > > > > Ron
                                > > > > > >
                                > > > > > > --- In MentalCalculation@yahoogroups.com, "dacastro93" wrote:
                                > > > > > > >
                                > > > > > > > Hi! I have a question for you...
                                > > > > > > >
                                > > > > > > > How can I calculate mentally high powers like, for example 41^23?
                                > > > > > > >
                                > > > > > > > I read that it can be achivied using logs, but the result will not be accurate: log41 ~ 1,6128, so log 41^23 will be 37,0944. Doing 41^23 in a calculator: =1,241734 x 10^37, but, with the use of antilog, I get 1,24280 x 10^37. How can I find precisely every single digit of the power? How many decimal places of logs will I need?
                                > > > > > > >
                                > > > > > > > And what about R�diger Gamm? Does he really have memorized the powers? Does he use mnemonics?
                                > > > > > > >
                                > > > > > > > Thank You in advance
                                > > > > > > >
                                > > > > > >
                                > > > > >
                                > > > >
                                > > >
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