Introducing Novel Geometric Insights and Three-Dimensional Depictions of the Pythagorean Theorem for any Triangles

Marco Aurélio Dos Santos Bernardes

doi:10.20944/preprints202402.1120.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 17 February 2024 / Approved: 20 February 2024 / Online: 20 February 2024 (09:00:36 CET)
Version 2 : Received: 7 April 2024 / Approved: 8 April 2024 / Online: 9 April 2024 (12:17:11 CEST)

The paper primarily demonstrates that the three internal triangles formed by connecting any point on a midsegment with the vertices of a generic triangle satisfy the geometric Proof of the Pythagorean theorem in Euclidean geometry. Moreover, this study elucidates the Pythagorean relationships inherent within three-dimensional geometric constructs resulting from the arrangement of three-dimensional spatial triangles. This geometric relationship, akin to a generalized extension of the Pythagorean theorem, unveils a unique spatial region characterized by this harmonious area interrelation among triangles.

Pythagorean theorem; three-dimensional space; triangles; three-dimensional geometric shape; Triangle Midsegment Theorem

Computer Science and Mathematics, Mathematics

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Introducing Novel Geometric Insights and Three-Dimensional Depictions of the Pythagorean Theorem for any Triangles

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