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Geometric Proof of the Tetrahedral Number Formula

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The tetrahedral numbers 1, 4, 10, 20, 35, are the sums of the triangular numbers,

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This Demonstration justifies the formula by showing 6 tetrahedra with sides forming an cuboid. The controls allow you to vary the side length of the tetrahedra from 1 to 5 and to vary the spacing between them.

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Contributed by: Jim Delany (March 2011)
Open content licensed under CC BY-NC-SA

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This idea was suggested by a remark in Jeffrey Stopple's A Primer of Analytic Number Theory: From Pythagoras to Riemann, New York: Cambridge University Press, 2003.

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