Lénárt, I. (2020) The Algebra of Projective Spheres on Plane, Sphere and Hemisphere. Journal of Applied Mathematics and Physics, 8, 2286-2333.
https://doi.org/10.4236/jamp.2020.810171

has been cited by the following article:

• TITLE: The Right Triangle as the Simplex in 2D Euclidean Space, Generalized to n Dimensions

  AUTHORS: István Lénárt

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

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.9, September 30, 2022

  ABSTRACT: 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.