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Re: [Mental Calculation] Can powers that end in powers be calculated?

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  • dacastro93
    Hello, Mr. Bouman, These patterns keep showing...12512+12488=25000 How did you find these numbers? Does this work for any power? I also would like to know
    Message 1 of 9 , Jan 22, 2013
    • 0 Attachment
      Hello, Mr. Bouman,

      These patterns keep showing...12512+12488=25000

      How did you find these numbers? Does this work for any power?

      I also would like to know where can I find a software able to compute higher numbers like 100^100. Does somebody know?

      Cheers,

      Daniel

      --- In MentalCalculation@yahoogroups.com, "A.W.A.P. Bouman" wrote:
      >
      > Good afternoon fellow calcualtors,
      >
      >
      >
      > The following number powered to 4 give 20736 at the end: 12, 12488, 12512,
      > 24988, 25012, 37488, 37512, 49988, 50012, 62488, 62512, 74988, 75012, 87488,
      > 87512, 99988.
      >
      >
      >
      > And: 316, 12184, 12816, 24684, 25316, 37184, 37816, 49684, 50316, 62184,
      > 62816, 74684, 75316, 87184, 87816, 99684.
      >
      >
      >
      > Best regards,
      >
      >
      >
      > Willem Bouman
      >
      >
      >
      >
      >
      >
      >
      > Van: MentalCalculation@yahoogroups.com
      > [mailto:MentalCalculation@yahoogroups.com] Namens Retothejuggler
      > Verzonden: dinsdag 22 januari 2013 9:20
      > Aan: MentalCalculation@yahoogroups.com
      > Onderwerp: Re: [Mental Calculation] Can powers that end in powers be
      > calculated?
      >
      >
      >
      >
      >
      > Hello Daniel
      >
      > Great one- maybe some CPU power could help to find more curiosities like
      > powers that end in squares or cubes? Can this be solved by mod arithmetics?
      >
      > Eg. which number powered can result in ...20736 at the end?
      >
      > --- In MentalCalculation@yahoogroups.com
      > , "dacastro93" wrote:
      > >
      > > Hi, Mr. Reto,
      > >
      > > He said in one of his videos that some number have these strange
      > properties. One example is 18^12 that starts with 34^2 = 1156. I think that
      > if we start looking deep into the numbers, we will find a lot of patterns,
      > which would help us with the memorization process.
      > >
      > > Cheers,
      > >
      > > Daniel
      > >
      > > --- In MentalCalculation@yahoogroups.com
      > , "Retothejuggler" wrote:
      > > >
      > > > Hello Willem
      > > >
      > > > Thanks for your input. I guess there is another interesting fact, some
      > numbers are coming up again and again but this only holds true for numbers
      > ending in 5.
      > > >
      > > > The regular two digit endings do not come to regular left side
      > begnnings, though :-).
      > > >
      > > > Kinders regards
      > > >
      > > > Reto
      > > >
      > > > --- In MentalCalculation@yahoogroups.com
      > , "A.W.A.P. Bouman" wrote:
      > > > >
      > > > > Good afternoon Reto,
      > > > >
      > > > >
      > > > >
      > > > > Although I am no clairvoyant, I have the feeling that the following is
      > > > > meant, and who is concerned : there is a clear structure in the
      > numbers when
      > > > > powering. Let's take 3 and restrict ourselves to the 2 last digits
      > when
      > > > > powering. Then we get: 01, 03, 09, 27 81, 43, 29, 87, 61, 83, 49, 47,
      > 41,
      > > > > 23, 69, 07, 21, 63, 89, 67 and again: 01, 03. So afer having built up
      > some
      > > > > experience one can feel what will come when powering and this can be
      > very
      > > > > helpful .
      > > > >
      > > > >
      > > > >
      > > > >
      > > > >
      > > > > Kindest regards,
      > > > >
      > > > >
      > > > >
      > > > >
      > > > >
      > > > > Willem Bouman
      > > > >
      > > > >
      > > > >
      > > > >
      > > > >
      > > > >
      > > > >
      > > > >
      > > > >
      > > > >
      > > > >
      > > > > Van: MentalCalculation@yahoogroups.com
      >
      > > > > [mailto:MentalCalculation@yahoogroups.com
      > ] Namens Retothejuggler
      > > > > Verzonden: zaterdag 19 januari 2013 12:33
      > > > > Aan: MentalCalculation@yahoogroups.com
      >
      > > > > Onderwerp: [Mental Calculation] Relationships between powers?
      > > > >
      > > > >
      > > > >
      > > > >
      > > > >
      > > > > This one still puzzles me:
      > > > >
      > > > > "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."
      > > > >
      > > > > What parts of numbers would you choose?
      > > > >
      > > > > Greetings from Switzerland
      > > > >
      > > > > Reto
      > > > >
      > > > >
      > > > >
      > > > >
      > > > >
      > > > > [Non-text portions of this message have been removed]
      > > > >
      > > >
      > >
      >
      >
      >
      >
      >
      > [Non-text portions of this message have been removed]
      >
    • A.W.A.P. Bouman
      Hi, Daniel, Well for 100^100 you do not need software, I suppose J. To be more serious: indeed there exists software for this kind of questions: academic
      Message 2 of 9 , Jan 22, 2013
      • 0 Attachment
        Hi, Daniel,



        Well for 100^100 you do not need software, I suppose J.



        To be more serious: indeed there exists software for this kind of questions: academic calculation programs, which will be very expensive and surely exceed the money you have in your purse, I have even heard of € 3.200!



        And indeed: you discovered the pattern. There is much, very much more to say about this. The world of the structure in the numbers is a magic world!! I am busy with describing my knowledge in my PC, momentally it concerns Modulo Calculation, very very interesting. Powering will certainly also be described, I have not yet a plan. After having finished the Modulo Calculation I could start with powering. The way I’ll publish this and when its all still in the stars.



        Best regards,



        Willem Bouman







        Van: MentalCalculation@yahoogroups.com [mailto:MentalCalculation@yahoogroups.com] Namens dacastro93
        Verzonden: dinsdag 22 januari 2013 16:48
        Aan: MentalCalculation@yahoogroups.com
        Onderwerp: Re: [Mental Calculation] Can powers that end in powers be calculated?





        Hello, Mr. Bouman,

        These patterns keep showing...12512+12488=25000

        How did you find these numbers? Does this work for any power?

        I also would like to know where can I find a software able to compute higher numbers like 100^100. Does somebody know?

        Cheers,

        Daniel

        --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman" wrote:
        >
        > Good afternoon fellow calcualtors,
        >
        >
        >
        > The following number powered to 4 give 20736 at the end: 12, 12488, 12512,
        > 24988, 25012, 37488, 37512, 49988, 50012, 62488, 62512, 74988, 75012, 87488,
        > 87512, 99988.
        >
        >
        >
        > And: 316, 12184, 12816, 24684, 25316, 37184, 37816, 49684, 50316, 62184,
        > 62816, 74684, 75316, 87184, 87816, 99684.
        >
        >
        >
        > Best regards,
        >
        >
        >
        > Willem Bouman
        >
        >
        >
        >
        >
        >
        >
        > Van: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
        > [mailto:MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com> ] Namens Retothejuggler
        > Verzonden: dinsdag 22 januari 2013 9:20
        > Aan: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
        > Onderwerp: Re: [Mental Calculation] Can powers that end in powers be
        > calculated?
        >
        >
        >
        >
        >
        > Hello Daniel
        >
        > Great one- maybe some CPU power could help to find more curiosities like
        > powers that end in squares or cubes? Can this be solved by mod arithmetics?
        >
        > Eg. which number powered can result in ...20736 at the end?
        >
        > --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
        > , "dacastro93" wrote:
        > >
        > > Hi, Mr. Reto,
        > >
        > > He said in one of his videos that some number have these strange
        > properties. One example is 18^12 that starts with 34^2 = 1156. I think that
        > if we start looking deep into the numbers, we will find a lot of patterns,
        > which would help us with the memorization process.
        > >
        > > Cheers,
        > >
        > > Daniel
        > >
        > > --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
        > , "Retothejuggler" wrote:
        > > >
        > > > Hello Willem
        > > >
        > > > Thanks for your input. I guess there is another interesting fact, some
        > numbers are coming up again and again but this only holds true for numbers
        > ending in 5.
        > > >
        > > > The regular two digit endings do not come to regular left side
        > begnnings, though :-).
        > > >
        > > > Kinders regards
        > > >
        > > > Reto
        > > >
        > > > --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
        > , "A.W.A.P. Bouman" wrote:
        > > > >
        > > > > Good afternoon Reto,
        > > > >
        > > > >
        > > > >
        > > > > Although I am no clairvoyant, I have the feeling that the following is
        > > > > meant, and who is concerned : there is a clear structure in the
        > numbers when
        > > > > powering. Let's take 3 and restrict ourselves to the 2 last digits
        > when
        > > > > powering. Then we get: 01, 03, 09, 27 81, 43, 29, 87, 61, 83, 49, 47,
        > 41,
        > > > > 23, 69, 07, 21, 63, 89, 67 and again: 01, 03. So afer having built up
        > some
        > > > > experience one can feel what will come when powering and this can be
        > very
        > > > > helpful .
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > > Kindest regards,
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > > Willem Bouman
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > > Van: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
        >
        > > > > [mailto:MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
        > ] Namens Retothejuggler
        > > > > Verzonden: zaterdag 19 januari 2013 12:33
        > > > > Aan: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
        >
        > > > > Onderwerp: [Mental Calculation] Relationships between powers?
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > > This one still puzzles me:
        > > > >
        > > > > "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."
        > > > >
        > > > > What parts of numbers would you choose?
        > > > >
        > > > > Greetings from Switzerland
        > > > >
        > > > > Reto
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > > [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
        Do you plan to publish in english? Cheers, Daniel
        Message 3 of 9 , Jan 22, 2013
        • 0 Attachment
          Do you plan to publish in english?

          Cheers,

          Daniel

          --- In MentalCalculation@yahoogroups.com, "A.W.A.P. Bouman" wrote:
          >
          > Hi, Daniel,
          >
          >
          >
          > Well for 100^100 you do not need software, I suppose J.
          >
          >
          >
          > To be more serious: indeed there exists software for this kind of questions: academic calculation programs, which will be very expensive and surely exceed the money you have in your purse, I have even heard of € 3.200!
          >
          >
          >
          > And indeed: you discovered the pattern. There is much, very much more to say about this. The world of the structure in the numbers is a magic world!! I am busy with describing my knowledge in my PC, momentally it concerns Modulo Calculation, very very interesting. Powering will certainly also be described, I have not yet a plan. After having finished the Modulo Calculation I could start with powering. The way I’ll publish this and when its all still in the stars.
          >
          >
          >
          > Best regards,
          >
          >
          >
          > Willem Bouman
          >
          >
          >
          >
          >
          >
          >
          > Van: MentalCalculation@yahoogroups.com [mailto:MentalCalculation@yahoogroups.com] Namens dacastro93
          > Verzonden: dinsdag 22 januari 2013 16:48
          > Aan: MentalCalculation@yahoogroups.com
          > Onderwerp: Re: [Mental Calculation] Can powers that end in powers be calculated?
          >
          >
          >
          >
          >
          > Hello, Mr. Bouman,
          >
          > These patterns keep showing...12512+12488=25000
          >
          > How did you find these numbers? Does this work for any power?
          >
          > I also would like to know where can I find a software able to compute higher numbers like 100^100. Does somebody know?
          >
          > Cheers,
          >
          > Daniel
          >
          > --- In MentalCalculation@yahoogroups.com , "A.W.A.P. Bouman" wrote:
          > >
          > > Good afternoon fellow calcualtors,
          > >
          > >
          > >
          > > The following number powered to 4 give 20736 at the end: 12, 12488, 12512,
          > > 24988, 25012, 37488, 37512, 49988, 50012, 62488, 62512, 74988, 75012, 87488,
          > > 87512, 99988.
          > >
          > >
          > >
          > > And: 316, 12184, 12816, 24684, 25316, 37184, 37816, 49684, 50316, 62184,
          > > 62816, 74684, 75316, 87184, 87816, 99684.
          > >
          > >
          > >
          > > Best regards,
          > >
          > >
          > >
          > > Willem Bouman
          > >
          > >
          > >
          > >
          > >
          > >
          > >
          > > Van: MentalCalculation@yahoogroups.com
          > > [mailto:MentalCalculation@yahoogroups.com ] Namens Retothejuggler
          > > Verzonden: dinsdag 22 januari 2013 9:20
          > > Aan: MentalCalculation@yahoogroups.com
          > > Onderwerp: Re: [Mental Calculation] Can powers that end in powers be
          > > calculated?
          > >
          > >
          > >
          > >
          > >
          > > Hello Daniel
          > >
          > > Great one- maybe some CPU power could help to find more curiosities like
          > > powers that end in squares or cubes? Can this be solved by mod arithmetics?
          > >
          > > Eg. which number powered can result in ...20736 at the end?
          > >
          > > --- In MentalCalculation@yahoogroups.com
          > > , "dacastro93" wrote:
          > > >
          > > > Hi, Mr. Reto,
          > > >
          > > > He said in one of his videos that some number have these strange
          > > properties. One example is 18^12 that starts with 34^2 = 1156. I think that
          > > if we start looking deep into the numbers, we will find a lot of patterns,
          > > which would help us with the memorization process.
          > > >
          > > > Cheers,
          > > >
          > > > Daniel
          > > >
          > > > --- In MentalCalculation@yahoogroups.com
          > > , "Retothejuggler" wrote:
          > > > >
          > > > > Hello Willem
          > > > >
          > > > > Thanks for your input. I guess there is another interesting fact, some
          > > numbers are coming up again and again but this only holds true for numbers
          > > ending in 5.
          > > > >
          > > > > The regular two digit endings do not come to regular left side
          > > begnnings, though :-).
          > > > >
          > > > > Kinders regards
          > > > >
          > > > > Reto
          > > > >
          > > > > --- In MentalCalculation@yahoogroups.com
          > > , "A.W.A.P. Bouman" wrote:
          > > > > >
          > > > > > Good afternoon Reto,
          > > > > >
          > > > > >
          > > > > >
          > > > > > Although I am no clairvoyant, I have the feeling that the following is
          > > > > > meant, and who is concerned : there is a clear structure in the
          > > numbers when
          > > > > > powering. Let's take 3 and restrict ourselves to the 2 last digits
          > > when
          > > > > > powering. Then we get: 01, 03, 09, 27 81, 43, 29, 87, 61, 83, 49, 47,
          > > 41,
          > > > > > 23, 69, 07, 21, 63, 89, 67 and again: 01, 03. So afer having built up
          > > some
          > > > > > experience one can feel what will come when powering and this can be
          > > very
          > > > > > helpful .
          > > > > >
          > > > > >
          > > > > >
          > > > > >
          > > > > >
          > > > > > Kindest regards,
          > > > > >
          > > > > >
          > > > > >
          > > > > >
          > > > > >
          > > > > > Willem Bouman
          > > > > >
          > > > > >
          > > > > >
          > > > > >
          > > > > >
          > > > > >
          > > > > >
          > > > > >
          > > > > >
          > > > > >
          > > > > >
          > > > > > Van: MentalCalculation@yahoogroups.com
          > >
          > > > > > [mailto:MentalCalculation@yahoogroups.com
          > > ] Namens Retothejuggler
          > > > > > Verzonden: zaterdag 19 januari 2013 12:33
          > > > > > Aan: MentalCalculation@yahoogroups.com
          > >
          > > > > > Onderwerp: [Mental Calculation] Relationships between powers?
          > > > > >
          > > > > >
          > > > > >
          > > > > >
          > > > > >
          > > > > > This one still puzzles me:
          > > > > >
          > > > > > "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."
          > > > > >
          > > > > > What parts of numbers would you choose?
          > > > > >
          > > > > > Greetings from Switzerland
          > > > > >
          > > > > > Reto
          > > > > >
          > > > > >
          > > > > >
          > > > > >
          > > > > >
          > > > > > [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 Daniel, Yes English, form y Chinese is not so good. Willem Van: MentalCalculation@yahoogroups.com [mailto:MentalCalculation@yahoogroups.com] Namens
          Message 4 of 9 , Jan 22, 2013
          • 0 Attachment
            Hi Daniel,



            Yes English, form y Chinese is not so good.



            Willem



            Van: MentalCalculation@yahoogroups.com [mailto:MentalCalculation@yahoogroups.com] Namens dacastro93
            Verzonden: dinsdag 22 januari 2013 20:23
            Aan: MentalCalculation@yahoogroups.com
            Onderwerp: Re: [Mental Calculation] Can powers that end in powers be calculated?





            Do you plan to publish in english?

            Cheers,

            Daniel

            --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman" wrote:
            >
            > Hi, Daniel,
            >
            >
            >
            > Well for 100^100 you do not need software, I suppose J.
            >
            >
            >
            > To be more serious: indeed there exists software for this kind of questions: academic calculation programs, which will be very expensive and surely exceed the money you have in your purse, I have even heard of € 3.200!
            >
            >
            >
            > And indeed: you discovered the pattern. There is much, very much more to say about this. The world of the structure in the numbers is a magic world!! I am busy with describing my knowledge in my PC, momentally it concerns Modulo Calculation, very very interesting. Powering will certainly also be described, I have not yet a plan. After having finished the Modulo Calculation I could start with powering. The way I’ll publish this and when its all still in the stars.
            >
            >
            >
            > Best regards,
            >
            >
            >
            > Willem Bouman
            >
            >
            >
            >
            >
            >
            >
            > Van: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com> [mailto:MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
            > Verzonden: dinsdag 22 januari 2013 16:48
            > Aan: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
            > Onderwerp: Re: [Mental Calculation] Can powers that end in powers be calculated?
            >
            >
            >
            >
            >
            > Hello, Mr. Bouman,
            >
            > These patterns keep showing...12512+12488=25000
            >
            > How did you find these numbers? Does this work for any power?
            >
            > I also would like to know where can I find a software able to compute higher numbers like 100^100. Does somebody know?
            >
            > Cheers,
            >
            > Daniel
            >
            > --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman" wrote:
            > >
            > > Good afternoon fellow calcualtors,
            > >
            > >
            > >
            > > The following number powered to 4 give 20736 at the end: 12, 12488, 12512,
            > > 24988, 25012, 37488, 37512, 49988, 50012, 62488, 62512, 74988, 75012, 87488,
            > > 87512, 99988.
            > >
            > >
            > >
            > > And: 316, 12184, 12816, 24684, 25316, 37184, 37816, 49684, 50316, 62184,
            > > 62816, 74684, 75316, 87184, 87816, 99684.
            > >
            > >
            > >
            > > Best regards,
            > >
            > >
            > >
            > > Willem Bouman
            > >
            > >
            > >
            > >
            > >
            > >
            > >
            > > Van: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
            > > [mailto:MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com> ] Namens Retothejuggler
            > > Verzonden: dinsdag 22 januari 2013 9:20
            > > Aan: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
            > > Onderwerp: Re: [Mental Calculation] Can powers that end in powers be
            > > calculated?
            > >
            > >
            > >
            > >
            > >
            > > Hello Daniel
            > >
            > > Great one- maybe some CPU power could help to find more curiosities like
            > > powers that end in squares or cubes? Can this be solved by mod arithmetics?
            > >
            > > Eg. which number powered can result in ...20736 at the end?
            > >
            > > --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
            > > , "dacastro93" wrote:
            > > >
            > > > Hi, Mr. Reto,
            > > >
            > > > He said in one of his videos that some number have these strange
            > > properties. One example is 18^12 that starts with 34^2 = 1156. I think that
            > > if we start looking deep into the numbers, we will find a lot of patterns,
            > > which would help us with the memorization process.
            > > >
            > > > Cheers,
            > > >
            > > > Daniel
            > > >
            > > > --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
            > > , "Retothejuggler" wrote:
            > > > >
            > > > > Hello Willem
            > > > >
            > > > > Thanks for your input. I guess there is another interesting fact, some
            > > numbers are coming up again and again but this only holds true for numbers
            > > ending in 5.
            > > > >
            > > > > The regular two digit endings do not come to regular left side
            > > begnnings, though :-).
            > > > >
            > > > > Kinders regards
            > > > >
            > > > > Reto
            > > > >
            > > > > --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
            > > , "A.W.A.P. Bouman" wrote:
            > > > > >
            > > > > > Good afternoon Reto,
            > > > > >
            > > > > >
            > > > > >
            > > > > > Although I am no clairvoyant, I have the feeling that the following is
            > > > > > meant, and who is concerned : there is a clear structure in the
            > > numbers when
            > > > > > powering. Let's take 3 and restrict ourselves to the 2 last digits
            > > when
            > > > > > powering. Then we get: 01, 03, 09, 27 81, 43, 29, 87, 61, 83, 49, 47,
            > > 41,
            > > > > > 23, 69, 07, 21, 63, 89, 67 and again: 01, 03. So afer having built up
            > > some
            > > > > > experience one can feel what will come when powering and this can be
            > > very
            > > > > > helpful .
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > > Kindest regards,
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > > Willem Bouman
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > > Van: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
            > >
            > > > > > [mailto:MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
            > > ] Namens Retothejuggler
            > > > > > Verzonden: zaterdag 19 januari 2013 12:33
            > > > > > Aan: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
            > >
            > > > > > Onderwerp: [Mental Calculation] Relationships between powers?
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > > This one still puzzles me:
            > > > > >
            > > > > > "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."
            > > > > >
            > > > > > What parts of numbers would you choose?
            > > > > >
            > > > > > Greetings from Switzerland
            > > > > >
            > > > > > Reto
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > > [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]
          • Gerald Newport
            Willem,   Please publish what you know and remember, neither of us is getting any younger.                     You have spent a lifetime adding to
            Message 5 of 9 , Jan 22, 2013
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              Willem,   Please publish what you know and remember, neither of us is getting any younger.                 

                 You have spent a lifetime adding to your natural talent. You will leave the world a great gift with a book of

              your knowledge about calculating.

                                                                                 Jerry Newport
            • Retothejuggler
              Dear Willem Thanks for your input. Can this be used for any power? Interesting... I`ll support a book and I`m sure other here as well. Respectful Reto
              Message 6 of 9 , Jan 23, 2013
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                Dear Willem

                Thanks for your input. Can this be used for any power? Interesting...

                I`ll support a book and I`m sure other here as well.

                Respectful

                Reto

                --- In MentalCalculation@yahoogroups.com, Gerald Newport wrote:
                >
                > Willem,   Please publish what you know and remember, neither of us is getting any younger.                 
                >
                >    You have spent a lifetime adding to your natural talent. You will leave the world a great gift with a book of
                >
                > your knowledge about calculating.
                >
                >                                                                    Jerry Newport
                >
              • A.W.A.P. Bouman
                Dear Gerald and Reto, Thank you for your encouraging words. I realise that I am getting older, to be precise: every day one piece. Describing what is going on
                Message 7 of 9 , Jan 23, 2013
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                  Dear Gerald and Reto,



                  Thank you for your encouraging words. I realise that I am getting older, to
                  be precise: every day one piece. Describing what is going on in my curly
                  head will take a lot of time. I hope it will be granted to me by the Lord
                  Almighty.



                  Best regards,



                  Willem



                  Van: MentalCalculation@yahoogroups.com
                  [mailto:MentalCalculation@yahoogroups.com] Namens Retothejuggler
                  Verzonden: woensdag 23 januari 2013 10:13
                  Aan: MentalCalculation@yahoogroups.com
                  Onderwerp: Re: [Mental Calculation] Can powers that end in powers be
                  calculated?





                  Dear Willem

                  Thanks for your input. Can this be used for any power? Interesting...

                  I`ll support a book and I`m sure other here as well.

                  Respectful

                  Reto

                  --- In MentalCalculation@yahoogroups.com
                  <mailto:MentalCalculation%40yahoogroups.com> , Gerald Newport wrote:
                  >
                  > Willem, Please publish what you know and remember, neither of us is
                  getting any younger.
                  >
                  > You have spent a lifetime adding to your natural talent. You will leave
                  the world a great gift with a book of
                  >
                  > your knowledge about calculating.
                  >
                  > Jerry
                  Newport
                  >





                  [Non-text portions of this message have been removed]
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