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A Visual Proof of Nicomachus's Theorem
Nicomachus's theorem states that , where is a positive integer. In words, the sum of the cubes from 1 to is equal to the square of the sum from 1 to .
For a visual proof, calculate the total area in the figure in two different ways: First, count the unit squares from the center to an edge to get , so that the total area is . Second, consider that each square ring consists of squares of side , with area .



"A Visual Proof of Nicomachus's Theorem" from The Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/AVisualProofOfNicomachussTheorem/
Contributed by: Michael Schreiber
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