TITLE:
The Insphere of a Tetrahedron
AUTHORS:
Peter Paul Klein
KEYWORDS:
Corkscrew Rule, Hesse Normal Form, Decomposed Linear System, Block Upper Triangular Form of Coefficient Matrix, Cofactor Matrix
JOURNAL NAME:
Applied Mathematics,
Vol.11 No.7,
July
20,
2020
ABSTRACT: A contiguous derivation of radius and center of the insphere of a general tetrahedron is given. Therefore a linear system is derived. After a transformation of it the calculation of radius and center can be separated from each other. The remaining linear system for the center of the insphere can be solved after discovering the inverse of the corresponding coefficient matrix. This procedure can also be applied in the planar case to determine radius and center of the incircle of a triangle.