Parametric proofs of the Pythagorean theorem via ziggurats and pyramids

Abstract

We present two parametric families of area-rearrangement proofs of the Pythagorean theorem. Our contribution is primarily constructive and expository: we organize the geometry through a single angular parameter. For certain appropriate parameters, we recover several known motifs as special instances. For less regular parameters, the argument becomes more complicated, requiring the use of trigonometric identities, a topic we also explore in further detail.

11 pages, 15 figures. This is a new version following the referees' comments