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Cubes and Squares

https://commons.wikimedia.org/wiki/File:Nicomachus_theorem_3D.svg
Image: Wikimedia Commons

MATLAB’s Loren Shure devised this lovely “proof without words” of Nicomachus’ theorem, that the sum of the first n cubes is the square of the nth triangular number:

\displaystyle 1^{3}+2^{3}+3^{3}+\cdots +n^{3}=\left(1+2+3+\cdots +n\right)^{2},

R.J. Stroeker of Erasmus University wrote, “Every beginning student of number theory surely must have marveled at [this] miraculous fact.”

December 23, 2019December 23, 2019 | Science & Math

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