%0 Journal Article
%T The Right Triangle as the Simplex in 2D Euclidean Space, Generalized to n Dimensions
%A Istv¨¢n L¨¦n¨¢rt
%J Journal of Applied Mathematics and Physics
%P 2837-2850
%@ 2327-4379
%D 2022
%I Scientific Research Publishing
%R 10.4236/jamp.2022.109189
%X 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 <em>n</em>-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.
%K Cycles of Incidence
%K Quadrirectangular Tetrahedron
%K Rectangular Pentachoron
%K Generalization of Pythagoras Theorem
%K Volume of a Rectangular Simplex
%K Cayley-Menger Determinant
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=120221