The authors present and prove the correctness of a geometric construction, stemming from Thales’ Theorem, that produces rectangles with length-to-width ratio (n+1) : n, for any positive integer n. These superparticular ratios, which include the most basic musical ratios, are important to those who study the relationships between art and math. The construction inherently involves a well-known family of Pythagorean triples, potentially in a novel way. The authors, one of whom is an artist, also present some examples of artwork inspired by Thales’ Theorem.