Author(s)

István Lénárt

ELTE University, Budapest, Hungary.

The purpose of the research is to show that the general triangle can be replaced by the right-angled triangle as the 2D simplex, and this concept can be generalized to any higher dimensions. The main results are that such forms do exist in any dimensions; meet the requirements usually placed on an n-dimensional simplex; a hypotenuse and legs can be defined in these shapes; and a formula can be given to calculate the volume of the shape solely from the legs by a direct generalization of the Pythagorean Theorem, without computing the Cayley-Menger determinant.

Cycles of Incidence, Quadrirectangular Tetrahedron, Rectangular Pentachoron, Generalization of Pythagoras Theorem, Volume of a Rectangular Simplex, Cayley-Menger Determinant

Lénárt, I. (2022) The Right Triangle as the Simplex in 2D Euclidean Space, Generalized to n Dimensions. Journal of Applied Mathematics and Physics, 10, 2837-2850. doi: 10.4236/jamp.2022.109189.