Generalized Pythagorean Theorem

Author(s)

Abstract
As we all know, Pythagorean theorem is aimed at right triangle. In this paper, Pythagorean theorem is extended to any triangle except equilateral triangle, generalized Pythagorean theorem is introduced, so that the so-called Pythagorean number becomes history and no longer exists, and it is very simple to judge whether a triangle is obtuse triangle, right triangle or acute triangle. According to the generalized Pythagorean theorem, the rank of a triangle,generalized sine and generalized cosine are introduced, so that when the rank of a triangle is known, the triangle can be solved as a right triangle; when the rank of a triangle is not known, a simple and direct method to solve the triangle is also obtained,and right now there is no necessary to use the sine theorem and cosine theorem as usual. Pythagorean theorem mainly studies straight and studies distance,but the generalized Pythagorean theorem can study skew. Finally, the geometric significance and theoretical significance of the rank of a triangle are given.

Keywords
generalized Pythagorean theorem，rank of triangle，generalized sine，generalized cosine

Cite this paper
Zhou Zhongwang, Generalized Pythagorean Theorem , SCIREA Journal of Mathematics. Volume 10, Issue 1, February 2025 | PP. 1-7. 10.54647/mathematics110515

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