Geometric Proof of the Tetrahedral Number Formula
The tetrahedral numbers 1, 4, 10, 20, 35, are the sums of the triangular numbers,[more]
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.[less]
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.