Fry's Geometric Demonstration of the Sum of Cubes

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The sum of the first cubes is given by the remarkable identity



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.


Contributed by: S. M. Blinder (January 2020)
Open content licensed under CC BY-NC-SA



[1] A. L. Fry, "Proof without Words: Sum of Cubes," Mathematics Magazine, 58(1), 1985 p. 11. doi:10.2307/2690228.

[2] D. Treeby, "Applying Archimedes's Method to Alternating Sums of Powers," The Mathematical Intelligencer, 40(4), 2018 pp. 65–70. doi:10.1007/s00283-018-9821-7.


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