The concept of the Euclidean simplex is important in the study of n-dimensional Euclidean geometry. This book introduces for the first time the concept of hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry. Following the emergence of his gyroalgebra in 1988, the author crafted gyrolanguage, the algebraic language t

chapter 1|18 pages


part |2 pages

PART I Einstein Gyrogroups and Gyrovector Spaces

chapter 2|52 pages

Einstein Gyrogroups

chapter 3|32 pages

Einstein Gyrovector Spaces

part |2 pages

PART II Mathematical Tools for Hyperbolic Geometry

chapter |40 pages

Gyroparallelograms and Gyroparallelotopes

chapter 7|69 pages


part |2 pages

PART III Hyperbolic Triangles and Circles

chapter 8|29 pages

Gyrotriangles and Gyrocircles

chapter 9|51 pages

Gyrocircle Theorems

part |2 pages

PART IV Hyperbolic Simplices, Hyperplanes and Hyperspheres in N Dimensions

chapter 10|108 pages

Gyrosimplex Gyrogeometry

chapter 11|36 pages

Gyrotetrahedron Gyrogeometry

part |2 pages

PART V Hyperbolic Ellipses and Hyperbolas

chapter 12|48 pages

Gyroellipses and Gyrohyperbolas

part |2 pages

PART VI Thomas Precession

chapter 13|24 pages

Thomas Precession

chapter |2 pages

Notations and Special Symbols