The Insphere of a Tetrahedron  

作　　者：Peter Paul Klein Peter Paul Klein(Computing Center, University of Technology Clausthal, Clausthal-Zellerfeld, Germany)

机构地区：[1]Computing Center, University of Technology Clausthal, Clausthal-Zellerfeld, Germany

出　　处：《Applied Mathematics》2020年第7期601-612,共12页应用数学（英文）

摘　　要：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.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.

关 键 词：Corkscrew Rule Hesse Normal Form Decomposed Linear System Block Upper Triangular Form of Coefficient Matrix Cofactor Matrix 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]