A Proof of the Pythagorean Theorem via Signed Projections of a Rotating Right Triangle

Abstract

This record contains the English and Japanese versions of “A Proof of the Pythagorean Theorem via Signed Projections of a Rotating Right Triangle,” together with the TeX source files and bibliography. The paper presents a proof of the Pythagorean theorem based on signed orthogonal projections of a rotating right triangle, full-turn averaging, and cancellation of the mixed term. The proof does not use the Cartesian distance formula, an inner-product projection formula, the law of cosines, or an explicit trigonometric representation. This record contains a preprint and its source materials. The English version is the canonical version; the Japanese version is the author's translation.