2Dec/104
New James Tanton video on sums of cubes
Have you ever wondered why the sum of the cubes of consecutive positive integers is always a square? The key to one visual proof lies in the humble multiplication table and in an array of square dots.
Here's a new video from James Tanton that shows in a remarkably elegant way that 1^3 + 2^3 + 3^3 + ... + n^3 = (1+2+3+...+n)^2.
And, you don't need to have very much of a background in Math to follow the proof. Absolutely amazing!
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December 3rd, 2010 - 04:16
thanks for this… WHERE was James Tanton when I was in school!! (and when do we clone him?)
December 3rd, 2010 - 07:19
That’s a fantastic post, I’m going to post this video too at some point; and a great blog, btw. Cheers, VMT
December 5th, 2010 - 10:59
I ff’ed the video, stopping to examine full boards of stuff.
One big chunk looked an awful lot like one of ways I help kids count rectangles on a chessboard.
Oh yeah, same thing really!
December 6th, 2011 - 07:15
When I was in school I always found these kind of problems very difficult. I wish we had you tube that time … life would have different