Fry's Geometric Demonstration of the Sum of Cubes
Fry's Geometric Demonstration of the Sum of Cubes
The sum of the first cubes is given by the remarkable identity
n
3
1
3
2
3
n
2
(1+2+…+n)
2
2
n
4
Fry [1, 2] gave a geometrical proof of this result based on the slicing of cubes into square slabs and their assembly into a × square. For an even summand, one of the square slabs is cut in half for each end of the L-shape.
k×k×k
k
k×k
n(n+1)
2
n(n+1)
2