# Geometric Proof of the Tetrahedral Number Formula

Geometric Proof of the Tetrahedral Number Formula

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

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T=1+3+6+10+…+t=(n+1)(n+2)(n+3)/6

n

n

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.

n

(n+1)×(n+2)×(n+3)