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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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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(n+1)×(n+2)×(n+3)