An Application of Einsteinian-Phythagorean Theorem in Einstein Gyrovector Spaces

Abstract

In [Ungar 2008; Ungar 2015] A.A. Ungar, employs the Einstein gyrovector spaces for the introduction of the gyrotrigonometry, Ungar’s and other researcher’s works play a major role in translating some theorems from Euclidean geometry to corresponding theorems in Einstein gyrovector spaces. In Euclidean geometry, the sum of the squares of the lengths of opposite sides of convex or concave quadrilaterals whose diagonals intersect perpendicularly is equal to each other. In this paper, we present this theorem in Einstein gyrovector spaces in terms of gamma factors.