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Journal for Geometry and Graphics 25 (2021), No. 2, 231--241
Copyright Heldermann Verlag 2021

On a Proof of the Thabit Ibn Qurra's Generalization of the Pythagorean Theorem

Giovanni Vincenzi
Dipartimento di Matematica, UniversitÓ di Salerno, Fisciano, Italy

One of the most interesting generalizations of the Pythagorean theorem was stated by Thabit in the IX century. However, as claimed an expert of history of mathematics the Arab mathematician did not present the proof, as it can likely be obtained by elementary properties regarding similar triangles. According to historical documents, it is challenging to establish whether a proof of Thabit's theorem exists based exclusively on equidecomposibility, as in the case of the Pythagorean and Pappus theorems. This article presents the corresponding proof.

Keywords: Euclidean geometry, generalization of Pythagorean theorem, equidecomposability, figure dissection, geometric construction.

MSC: 51M15; 97G30.

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