Thales’ Theorem, Pythagorean Triples, and Geometric Art

Year: 2022 Authors: Stephen R. Wassell; Mark A. Reynolds

Core claim

A simple straightedge-and-compass construction derived from Thales’ Theorem generates every superparticular rectangle (n + 1):n and embeds the family of Pythagorean triples on the unit circle.

Topics

Thales’ Theorem, Pythagorean triples, superparticular ratios, geometric construction

Domains

Euclidean geometry, number theory, ratio theory, unit circle parameterization, geometric art, mathematical drawing, visual composition, art-math collaboration

Methods

straightedge-and-compass construction, algebraic verification, circle symmetry, rational-point parameterization

Media

unit circle, rectangles, drawings, colored line artwork

Source status

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