The method of undetermined coefficients may lead to a circular argument when attempting to prove that the square of the hypotenuse in a right triangle is a function of the lengths of the other two sides. Dimensional analysis of the square of a length ensures that the square of the hypotenuse in a right triangle can be expressed as the sum of the squares of the other two sides, without including first-order terms of these side lengths. Dimensional analysis is also an important method in physics and is therefore an appropriate subject for cross-disciplinary learning between mathematics and physics.

Pythagorean theorem, similarity, physical quantity, dimensional analysis

Received: September 1, 2024; Accepted: October 29, 2024; Published: November 25, 2024

How to cite this article: Yukio Kobayashi, Supplementary remarks on a weak proof of the Pythagorean theorem – from the viewpoint of dimensional analysis of physical quantities, Far East Journal of Mathematical Education 27(1) (2025), 1-10. https://doi.org/10.17654/0973563125001

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] Chuya Fukuda, A weak proof of the Pythagorean theorem, Far East Journal of Mathematical Education 26(1) (2024), 15-16.
[2] International Union of Pure and Applied Chemistry, Quantities, Units and Symbols in Physical Chemistry, IUPAC, 2007.
[3] Yukio Kobayashi, Supplementary remarks on simple sum using dimensions - from viewpoint of connection to physics based on weighted average, Far East Journal of Mathematical Education 26(1) (2024), 55-70.