Physics and the Pythagorean Theorem

TL;DR

This paper explores the historical origins of the Pythagorean theorem, presents a pictorial proof possibly from ancient China, and discusses its fundamental role and generalizations in modern physics and potential links to unified theories.

Contribution

It uncovers a possible ancient pictorial proof of the Pythagorean theorem and discusses its generalizations that underpin key physical laws and theories.

Findings

A pictorial proof may date back to the Zhou Dynasty.

Generalizations of the theorem relate to energy-momentum and field equations.

The theorem's pre-mathematical nature supports philosophical views on the mind-stuff of the universe.

Abstract

Pythagoras' theorem lies at the heart of physics as well as mathematics, yet its historical origins are obscure. We highlight a purely pictorial, gestalt-like proof that may have originated during the Zhou Dynasty. Generalizations of the Pythagorean theorem to three, four and more dimensions undergird fundamental laws including the energy-momentum relation of particle physics and the field equations of general relativity, and may hint at future unified theories. The "pre-mathematical" nature of this theorem lends support to the Eddingtonian view that "the stuff of the world is mind-stuff."