Generalizations of Pythagoras’ Theorem

Abstract

Pythagoras’ Theorem is one of the most fascinating results in the History of Mathematics. Although there are indications that the result was already known before by the Babylonians, was with the Pythagorean School that there was a formal demonstration of this theorem. As Loomis (1972), in 1940 were known at least 340 different demonstrations of the Pythagoras’ Theorem, whose enunciation is as follows: “In any right triangle, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares whose sides are over each cathetus”. This article discusses Pythagoras’ Theorem and some generalizations, and introduces a new generalization of this important theorem.