Analytic Hyperbolic Geometry in N Dimensions : An Introduction

This book introduces for the first time the hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry. The extension of common Euclidean geometry to N dimensions, with N being any positive integer, results in greater generality and succinctness in related expressions. Using new mathematical tools, the book demonstrates that this is also the case with analytic hyperbolic geometry. For example, the author analytically determines the hyperbolic circumcenter and circumradius of any hyperbolic simplex.