PROOF WITHOUT WORDS: SUMS OF SUMS OF SQUARES
A pictorial proof of the Sums of Sums of Squares, that is,
(Tk : Triangular Number), is provided. By expressing each square number as a sum of consecutive odd numbers, we can place those odd numbers into a tetrahedron. And if we change the base of this tetrahedron four times, we get four tetrahedrons. By summing up the corresponding parts of these four tetrahedrons, the Sums of Sums of Squares can be expressed as the formula shown above.
square number, consecutive odd numbers, tetrahedron.
Received: December 2, 2022; Accepted: December 10, 2022; Published: December 19, 2022
How to cite this article: Chuya Fukuda, Proof without words: sums of sums of squares, Far East Journal of Mathematical Education 24 (2023), 7-8. http://dx.doi.org/10.17654/0973563123003
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
