Uma visão vetorial do Teorema de Pitágoras no tetraedro via matriz de Gram

Abstract

The Pythagorean Theorem is undoubtedly one of the most fundamental pillars of Euclidean geometry, with numerous proofs and practical applications throughout the history of mathematics. This work proposes a theoretical approach to its proof in three-dimensional space: De Gua's Theorem. The research is based on a vectorial perspective, using the Gram Matrix as a central tool to demonstrate the relationship between the areas of the faces of a trirectangular tetrahedron. With the purpose of performing a didactic transposition aimed at the school environment in basic education, the Educational Product entitled "Pythagoras 3D: The Geometry of the Corner of the Room" was developed