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arXiv · 2511.00089

Parametric proofs of the Pythagorean theorem via ziggurats and pyramids

Andrés Navas
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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.

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Andrés Navas. 2025-10-30. Parametric proofs of the Pythagorean theorem via ziggurats and pyramids. https://arxiv.org/abs/2511.00089

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