Geodesic
On a Proof of the Thabit Ibn Qurra's Generalization of the Pythagorean Theorem
Journal for geometry and graphics, Tome 25 (2021) no. 2, pp. 231-241
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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 According to historical documents, it is challenging to establish whether a proof of Thabit's theorem exists based exclusively on equidecomposibility, as in the case of the Pythagorean and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.
Classification : 51M15, 97G30
Mots-clés : Euclidean geometry, generalization of Pythagorean theorem, equidecomposability, figure dissection, geometric construction 
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     author = {G. Vincenzi},
     title = {On a {Proof} of the {Thabit} {Ibn} {Qurra's} {Generalization} of the {Pythagorean} {Theorem}},
     journal = {Journal for geometry and graphics},
     pages = {231--241},
     year = {2021},
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G. Vincenzi. On a Proof of the Thabit Ibn Qurra's Generalization of the Pythagorean Theorem. Journal for geometry and graphics, Tome 25 (2021) no. 2, pp. 231-241. http://geodesic.mathdoc.fr/item/JGG_2021_25_2_JGG_2021_25_2_a6/