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#32
05-12-2005, 07:37 PM
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Re: Cool math shortcuts
[ QUOTE ]
[ QUOTE ] [ QUOTE ] [ QUOTE ] Heres an easy way to add up a sequence of numbers. For example, lets say from 1 to 100. 1 + 2 + 3 + 4 + 5 + 6 ..... + 100 = ? The sum of the first and last number, which is 1 + 100 = 101. The sum of the second and second to last number, which is 2 + 99 = 101. The sum of the third and third to last number, which is 3 + 98 = 101. Get the pattern? Summation of two numbers that equal 101 occurs 50x in this sequence. 1+100, or 2+99, or 3+98, or 4+97, or 5+96... 1 + 2 + 3 + 4 + 5 + 6 + 7 .... + 100 = 101 x 50 = 5050 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 11 x 5 = 55 Summation of 1 to 1000 = 1001 x 500 = 50050 17 to 9862 = 9879 x 4923 = 48,634,317 Its a neat idea, and could be fairly useful... [/ QUOTE ] Good job Gauss. [/ QUOTE ] well hey, no one ever said it was an original shortcut... [img]/images/graemlins/grin.gif[/img] [/ QUOTE ] Gauss came up with it when he was five. [/ QUOTE ] I guess you are familar with the story of how one of his teachers gave the same problem to his class to occupy them for awhile, and he solved it right away using the method I just explained. Blah... [img]/images/graemlins/tongue.gif[/img] 
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#33
05-12-2005, 07:42 PM
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Re: Cool math shortcuts
[ QUOTE ]
[ QUOTE ] Gauss came up with it when he was five. [/ QUOTE ] I love this story. Is it really true? [/ QUOTE ] Well, ever since E.T. Bell's book Men of Mathematics it is a major part of mathematical folklore.
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#34
05-12-2005, 07:46 PM
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Re: Cool math shortcuts
[ QUOTE ]
[ QUOTE ] [ QUOTE ] Gauss came up with it when he was five. [/ QUOTE ] I love this story. Is it really true? [/ QUOTE ] Well, ever since E.T. Bell's book Men of Mathematics it is a major part of mathematical folklore. [/ QUOTE ] I think I read it in some book about all these physics dudes. Hmm, En was the name or something. Lousy book. That's when I told my teacher I wasn't doing any more physics work and that I would be occupying all my time working on fantasy baseball. I rule.
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#35
05-12-2005, 07:47 PM
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Re: Cool math shortcuts
[ QUOTE ]
[ QUOTE ] [ QUOTE ] [ QUOTE ] [ QUOTE ] Heres an easy way to add up a sequence of numbers. For example, lets say from 1 to 100. 1 + 2 + 3 + 4 + 5 + 6 ..... + 100 = ? The sum of the first and last number, which is 1 + 100 = 101. The sum of the second and second to last number, which is 2 + 99 = 101. The sum of the third and third to last number, which is 3 + 98 = 101. Get the pattern? Summation of two numbers that equal 101 occurs 50x in this sequence. 1+100, or 2+99, or 3+98, or 4+97, or 5+96... 1 + 2 + 3 + 4 + 5 + 6 + 7 .... + 100 = 101 x 50 = 5050 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 11 x 5 = 55 Summation of 1 to 1000 = 1001 x 500 = 50050 17 to 9862 = 9879 x 4923 = 48,634,317 Its a neat idea, and could be fairly useful... [/ QUOTE ] Good job Gauss. [/ QUOTE ] well hey, no one ever said it was an original shortcut... [img]/images/graemlins/grin.gif[/img] [/ QUOTE ] Gauss came up with it when he was five. [/ QUOTE ] I guess you are familar with the story of how one of his teachers gave the same problem to his class to occupy them for awhile, and he solved it right away using the method I just explained. Blah... [img]/images/graemlins/tongue.gif[/img] [/ QUOTE ] Yeah, there are some other pretty remarkable stories about Gauss. Another story goes like this: his father owned a business. When he was three, Gauss was watching his father compute taxes and was just standing there constantly correcting his father. That's wrong, nope that's wrong, etc. When he was 15, he discovered the statement of the prime number theorem which explains the distribution of the primes (although failed to prove it) and when he was 17 he proved the fundamental theorem of algebra (every polynomial has a root) which had been unproven for hundreds of years.
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#36
05-12-2005, 07:53 PM
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Re: Cool math shortcuts
while we are on the subject, there is an easy way to do square root. for instance, if you wanted to find the square root of 9 you could do the following formula in your head:
a= your number^2 b= a(2) c= b(2) d= c(7)/b^2 ab^2+cd/(b/3^2)(cd/abc)^2=x x = 3
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#37
05-12-2005, 07:54 PM
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Re: Cool math shortcuts
[ QUOTE ]
[ QUOTE ] [ QUOTE ] [ QUOTE ] [ QUOTE ] [ QUOTE ] Heres an easy way to add up a sequence of numbers. For example, lets say from 1 to 100. 1 + 2 + 3 + 4 + 5 + 6 ..... + 100 = ? The sum of the first and last number, which is 1 + 100 = 101. The sum of the second and second to last number, which is 2 + 99 = 101. The sum of the third and third to last number, which is 3 + 98 = 101. Get the pattern? Summation of two numbers that equal 101 occurs 50x in this sequence. 1+100, or 2+99, or 3+98, or 4+97, or 5+96... 1 + 2 + 3 + 4 + 5 + 6 + 7 .... + 100 = 101 x 50 = 5050 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 11 x 5 = 55 Summation of 1 to 1000 = 1001 x 500 = 50050 17 to 9862 = 9879 x 4923 = 48,634,317 Its a neat idea, and could be fairly useful... [/ QUOTE ] Good job Gauss. [/ QUOTE ] well hey, no one ever said it was an original shortcut... [img]/images/graemlins/grin.gif[/img] [/ QUOTE ] Gauss came up with it when he was five. [/ QUOTE ] I guess you are familar with the story of how one of his teachers gave the same problem to his class to occupy them for awhile, and he solved it right away using the method I just explained. Blah... [img]/images/graemlins/tongue.gif[/img] [/ QUOTE ] Yeah, there are some other pretty remarkable stories about Gauss. Another story goes like this: his father owned a business. When he was three, Gauss was watching his father compute taxes and was just standing there constantly correcting his father. That's wrong, nope that's wrong, etc. When he was 15, he discovered the statement of the prime number theorem which explains the distribution of the primes (although failed to prove it) and when he was 17 he proved the fundamental theorem of algebra (every polynomial has a root) which had been unproven for hundreds of years. [/ QUOTE ] Lots of mathematicians seem to have interesting stories. I remember in high school when I got bored in math class, I would flip through the book and read the short biographies on mathematicians that they would have every couple of sections. I think I recall reading the same stories of Gauss correcting his dads computations and the story of adding up 1 to 100 in class.
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#38
05-12-2005, 08:17 PM
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Re: Cool math shortcuts
[ QUOTE ]
[ QUOTE ] Yeah, there are some other pretty remarkable stories about Gauss. Another story goes like this: his father owned a business. When he was three, Gauss was watching his father compute taxes and was just standing there constantly correcting his father. That's wrong, nope that's wrong, etc. When he was 15, he discovered the statement of the prime number theorem which explains the distribution of the primes (although failed to prove it) and when he was 17 he proved the fundamental theorem of algebra (every polynomial has a root) which had been unproven for hundreds of years. [/ QUOTE ] Lots of mathematicians seem to have interesting stories. I remember in high school when I got bored in math class, I would flip through the book and read the short biographies on mathematicians that they would have every couple of sections. I think I recall reading the same stories of Gauss correcting his dads computations and the story of adding up 1 to 100 in class. [/ QUOTE ] My personal favorite is about G.H. Hardy. Hardy was an English mathematician who worked in classical analysis and analytic number theory. One of the problems he devoted tremendous effort to is the Riemann Zeta problem. This problem is still unsolved today, as it has been for ~150 years. It's almost surely the most famous unsolved math problem. You may have heard of it as it's been covered in the NY Times a few times in the past two years, PBS has done a series on it and there are two popular math books published in the past two years on it. The Clay Mathematics Institute is offering one million dollars to the first mathematician to solve it. Hardy liked to travel. He took a trip to Denmark once to see Harold Bohr (mathematician brother of the physicist Niels Bohr). He was to travel back to England by sea but the North Sea is notoriously dangerous and the forecast was particularly bad. Hardy was a devout athiest but believed that God had a personal grudge against Hardy(!). Hardy believed this so firmly that he believed God wanted Hardy to have no glory. So Hardy wrote a postcard to his friend J. Littlewood saying "Riemann Zeta hypothesis. I have proven it. Details when I return. Regards, G.H." The idea being that the mathematical community would believe Hardy but God wouldn't cause Hardy's ship to sink because Hardy would die with the glory of having the world believe he solved the Riemann Zeta problem.
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