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Can anyone share what training methods they use to increase their
proficiency at calculating, I want to know if factorization can be
used as a means of practice. and how to do so if possible. what are in
your oppinion the best ways to train in the art of calculation, please
try to be as specific as possible,
thank you,
nathaniel
D. 0 Attachment
Hello there!!
Since last year i use this 'Speed math' program that i found in this
page:
http://www.jimmyr.com/blog/Speed_Math_Trainer_Program_126_2006.php
it's for free and it helped me improve a lot my mental calculation
skills. It's great especially for beginners and intermediate mental
calculators as me. Too bad it has n't got got any 8x8 multiplication
because some people especially in this page would found it helpful.
Hope i 've helped. Cheers.
Nodas Boukovalas. 0 Attachment
Dear Mr or Mrs 09,
As I do not like to correspond with numbers but with persons, I do not answer. I have an extensive experience with factorization, so if you are intersted, I want to have a personnal idendity.
Regards,
Willem Bouman
 Oorspronkelijk bericht 
Van: mentalmath09
Aan: MentalCalculation@yahoogroups.com
Verzonden: donderdag 3 januari 2008 14:31
Onderwerp: [Mental Calculation] Good Training Methods
Can anyone share what training methods they use to increase their
proficiency at calculating, I want to know if factorization can be
used as a means of practice. and how to do so if possible. what are in
your oppinion the best ways to train in the art of calculation, please
try to be as specific as possible,
thank you,
nathaniel
D.
[Nontext portions of this message have been removed] 0 Attachment
Mr.Bouman I am very Interested in what you know about factorization,
My Name is Nathaniel Day and i am quite young as a 15 year old, i
would be very thankfull if you could help to direct me in the right
direction as to how to practice, since i could use your wisdom. Since
i am begining the art of calculation at the same age that a.c atiken
began, and because i have a naturaly good memory for numbers i think i
can become very skilled in mental calculation. I would like however to
know the most efficient way to train, if there is such a thing, this
is only so that i dont wast my time practicing in a way that will not
help me at all. i am willing to train as many hours a day as need be.
so tell me what exercises can be used to develope a formidable ability
to calculate.
thank you,
Nathaniel Day 0 Attachment
Dear Nathaniel,
To begin: you have a meaningful biblic name, thank your parents for giving it!!
I mark your message as being not read for not to forget. It will take me much time to compose a useful answer to you, so please give me the time and opportunity. And if within a month you do not have your answer, you can send me a reminder "please do not forget Nathaniël".
Regards,
Willem Bouman
 Oorspronkelijk bericht 
Van: mentalmath09
Aan: MentalCalculation@yahoogroups.com
Verzonden: donderdag 3 januari 2008 19:47
Onderwerp: Re: [Mental Calculation] Good Training Methods
Mr.Bouman I am very Interested in what you know about factorization,
My Name is Nathaniel Day and i am quite young as a 15 year old, i
would be very thankfull if you could help to direct me in the right
direction as to how to practice, since i could use your wisdom. Since
i am begining the art of calculation at the same age that a.c atiken
began, and because i have a naturaly good memory for numbers i think i
can become very skilled in mental calculation. I would like however to
know the most efficient way to train, if there is such a thing, this
is only so that i dont wast my time practicing in a way that will not
help me at all. i am willing to train as many hours a day as need be.
so tell me what exercises can be used to develope a formidable ability
to calculate.
thank you,
Nathaniel Day
[Nontext portions of this message have been removed] 0 Attachment
Dear Nathaniël,
Calculation CV A.W.A.P. Bouman
Birth date 19091939. As a child of 2 years I knew the alphabet, being 3 years I could read the clock. At school 4 th class I knew all the 2×2 multiplications, they flew into my memory. At secondary school 1953 we learnt square roots. There the idea of sorting squares on same end figures: the squares of 7, 43, 57 and 93 all end on 49. Besides : 7+93=100, 43+57=100 43+50=93 and 7+70=57. After that the idea of sorting on 3 end figures struck me. 7,243,257, 493,507, 743,757 and 993, all their squares end on 049. After that all the squares till 1.000 were saved in my memory. This enabled me to do sqrts of numbers of 10 digits. About a year later I found a method for cubic roots, of numbers of 15 digits. In 1957 I got my school certificate, not on the mathematic department but on the commercial department. My mathematics are very weak. I am no mathematician, I am an arithmetician. It is a regrettable mistake that very good calculators automatically are very good mathematicians. Concerning me: even in the contrary.
During the sqrt period a mathematician attended me that a certain number is divisible, eg when it can be written as twice the sum of 2 squares. Mind you: in 1953 there was no internet, books about calculation I could not find. Example: 65= 7²+4² and 8²+1². This means 65 is divisible and the 2 factors themselves are the sum of 2 squares. To find the factors is  in this case  not very difficult, but there is a general formula for it. You take the even factors 8 and for and do (8±4)/2 and you get 6 and 2. Then you take (7±1)/2 and you get 4 and 3. the common factor of 6 and 4 is 2, the common factor of 3 and 2 is 1. the factors of 65 are by consequence 3²+2²= 13 and 2²+1²=5. Correct, isn'ít?
We take another example. To find out if this number is divisible we have to examine if this number can be written as twice the sum of 2 squares. Surprise, surprise: it is! 22²+3²= 493 and 18²+13²= 493. (22±18)/2=20 and 2 (13±3)/2= 8 and 5. 20 and 8 have common factor 4 and it goes 5 and 2 times, 5 and 2 have common factor 1 and it goes 5+2 times. So the factors of 493 are 5²+2²= 29 and 4²+1²=17.
So it works. Once having the right taste of it I made a sport of it to examine if a number is divisible. Knowing all the squares from 1 1.000 I could work with 6 digit numbers. EG the phone of my company was 429833, a very tough one. As you can compose 33 by many different ways, I doubled it to 859666. Now it was to figure out if there were 2 sets of squares to compose. After very very long searching I found: 879²+295² and 771²+515². They had to be reduced to resp. 587²+292² and 643² and 128². Now we do (643±587)/2 , so 615 and 28 and (292±128)/2 = 210 and 82. 615 and 210 have common factor 15, resp 41 and 14 times, 82 and 28 have common factor 2 and it goes  of course 41 and 14 times. Now the factors of 429833 are 41²+14²=1877 and the other one is 15²+2²=229 and please check if I gulled you.
During my working period calculation was a useful accessory, unfortunately I could not find other ones who did the same thing. One  very important  exception was my meeting with the famous Wim Klein in December 1959. There was something very amusing: in his opinion cubic roots by MC was impossible. After my demonstration and explanation he immediately understood my method.
I did nothing with my MC  why should I having no colleges and Klein lived in Switzerland. When I wanted to renew the contact in 1986 he was murdered shortly before.
The squares sport has never left me, so factorisation is my speciality. In Gießen at the MCWC in 2006 I was the only one with the full 100 points score on the prime numbers. In the MSO in England there are always ± 8 numbers of which to find the prime factors.
Now the use. Finding prime numbers is very important for encryption , eg on internet banking and other important questions of keeping secrets. A message is coded and only the recipient can decode, which is a prime number. How to find if a number is prime? The solution is take the sqrt of it and try if the number is divisible by one of the prime numbers under the sqrt.
Example: 527, is it divisible? Anyhow: it can never be written as the sum of 2 squares, being 7(8). Sqrt= max 22, for 23²=529. Prime numbers under 22 are: 2,3,5,7,11,13,17, and 19. Now divide 527 by all the prime numbers we have. You will find 17, it goes 31 times.
Now imagine you have a prime number of 100 digits. There are about 10^90 prime numbers, estimation. There is a computer which can do 10.000 calculations in a second. This is 10^86 seconds. A year has 31.536.000 seconds. This means about 10^78 years, widely exceeding a human life, isn't it?
So for me in personal point of view factorisation is very interesting it gives me insight in the number world, I steadily train the squares to compose numbers.
So far for today.
A good and trained memory is very important, no doubt about it. But an allround insight is at least as important.
For training I can advise you warmly the Georges Training Files in the Mental Calculation Group. And take your time, you are still very young. Let accuracy prevail above speed. And try to develop yourself as widely as possible.
Success!
Willem Bouman
 Oorspronkelijk bericht 
Van: mentalmath09
Aan: MentalCalculation@yahoogroups.com
Verzonden: donderdag 3 januari 2008 19:47
Onderwerp: Re: [Mental Calculation] Good Training Methods
Mr.Bouman I am very Interested in what you know about factorization,
My Name is Nathaniel Day and i am quite young as a 15 year old, i
would be very thankfull if you could help to direct me in the right
direction as to how to practice, since i could use your wisdom. Since
i am begining the art of calculation at the same age that a.c atiken
began, and because i have a naturaly good memory for numbers i think i
can become very skilled in mental calculation. I would like however to
know the most efficient way to train, if there is such a thing, this
is only so that i dont wast my time practicing in a way that will not
help me at all. i am willing to train as many hours a day as need be.
so tell me what exercises can be used to develope a formidable ability
to calculate.
thank you,
Nathaniel Day
[Nontext portions of this message have been removed] 0 Attachment
Thank You Mr.Bouman your message is very important to me, And i
learned a lot from it. I will practice doing the sport of
factorization and i began calculating squares of numbers to commit
them to memory. for use in factorizing. It is very impressive that you
committed to memory all of the 2x2 multiplications at such a early
age. Thank you again for all the information you shared with me about
factorization i found it very interesting and will certainly use the
knowledge you gave to me!
thank you,
Nathaniel Day 0 Attachment
Well Nathanaël,
If later studies bring you to further questions, I am always willing to help you.
Regards and success,
Willem Bouman
 Original Message 
From: mentalmath09 <mentalmath09@...>
To: MentalCalculation@yahoogroups.com
Sent: Saturday, 5 January, 2008 7:10:03 PM
Subject: Re: [Mental Calculation] Good Training Methods
Thank You Mr.Bouman your message is very important to me, And i
learned a lot from it. I will practice doing the sport of
factorization and i began calculating squares of numbers to commit
them to memory. for use in factorizing. It is very impressive that you
committed to memory all of the 2x2 multiplications at such a early
age. Thank you again for all the information you shared with me about
factorization i found it very interesting and will certainly use the
knowledge you gave to me!
thank you,
Nathaniel Day
__________________________________________________________
Sent from Yahoo! Mail  a smarter inbox http://uk.mail.yahoo.com
[Nontext portions of this message have been removed] 0 Attachment
Dear Mr Bouman,
If you were to ask me how I memorised the single digit multiplication
tables I could not provide a full answer because I am unsure having
remembered them so long ago as a child. This may also be the case with
your knowledge of the 2 digit tables considering how you remembered
them as a child as well. However is there any advice you can give me
on how I might do so. Should I factorise? Practice with certain
numbers (like primes)? I would prefer it if I did not have to try with
these so I can increase my speed with 8 by 8s.
Regards, jsh 0 Attachment
Dear Mr. Joshua(??)
We have the same question: you should bring me in a great embarrassment when asking "how did these 2×2 multiplications get saved in your brain?"
I can assure you that I never made a list of it and learnt them by heart. Certainly that at that age on school it was a daily matter, so the training was intensive.
Of course you should have basic knowledge immediately ready. Mine is only all multiplications 2×2, all squares 11.000 and the cubics of 1100. This is not very impressive  I know  but making a use as good as possible one can make a lot out of it.
I never learnt the primes till 10.000 by heart, but as I from a young boy till now make the "squares game" for factorisation I raher quickly recognise a prime number.
When you do your 8×8 multiplications with 1 digit at a time: continue with it, really. Wim Klein taught me the 2 digit method, I command the theory, the practice is very unmanageable. I consider myself yet too old 68 years to start with 1×1 digit, so I train as a fool to improve my results with 2×2.
And again and again: do not aim firstly at speed but at accuracy, let the pleasure in calculating not be poisoned by the watch.
Wim Klein made a lot of problems not only for other people but more still for himself by always trying to increase his speed, which was already inconvincible.
Regards,
Willem Bouman
 Oorspronkelijk bericht 
Van: jsh.flynn
Aan: MentalCalculation@yahoogroups.com
Verzonden: dinsdag 8 januari 2008 9:58
Onderwerp: Re: [Mental Calculation] Good Training Methods
Dear Mr Bouman,
If you were to ask me how I memorised the single digit multiplication
tables I could not provide a full answer because I am unsure having
remembered them so long ago as a child. This may also be the case with
your knowledge of the 2 digit tables considering how you remembered
them as a child as well. However is there any advice you can give me
on how I might do so. Should I factorise? Practice with certain
numbers (like primes)? I would prefer it if I did not have to try with
these so I can increase my speed with 8 by 8s.
Regards, jsh
[Nontext portions of this message have been removed] 0 Attachment
Re:
Thank you for your response. I think I remember Wim Klein calling
intentional memorisation mechanical memory, I would certainly favour
exposure and recognition to that (i.e. recognising combinations of
factors and having an intuition for solutions). I to have a lot of
facts readily available (powers of two digit numbers and division
tables), the trouble is you can't just keep adding fact after fact,
with numbers it takes years of maintenance to have something
permanently stored in long term memory.
Regards, Josh
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