Analytic Hyperbolic Geometry in N Dimensions

An Introduction

Abraham Albert Ungar (North Dakota State University, Fargo, USA)

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English

CRC Press Inc
17 December 2014

Number theory; Analytic geometry; Mathematical physics

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 that sheds natural light on hyperbolic geometry and special relativity. Several authors have successfully employed the author’s gyroalgebra in their exploration for novel results. Françoise Chatelin noted in her book, and elsewhere, that the computation language of Einstein described in this book plays a universal computational role, which extends far beyond the domain of special relativity.

This book will encourage researchers to use the author’s novel techniques to formulate their own results. The book provides new mathematical tools, such as hyperbolic simplexes, for the study of hyperbolic geometry in n dimensions. It also presents a new look at Einstein’s special relativity theory.

By: Abraham Albert Ungar (North Dakota State University Fargo USA)
Imprint: CRC Press Inc
Country of Publication: United States
Dimensions: Height: 234mm, Width: 156mm, Spine: 36mm
Weight: 975g
ISBN: 9781482236675
ISBN 10: 1482236672
Pages: 624
Publication Date: 17 December 2014
Audience: General/trade , College/higher education , ELT Advanced , Primary
Format: Hardback
Publisher's Status: Active

List of Figures. Preface. Author’s Biography. Introduction. Einstein Gyrogroups and Gyrovector Spaces. Einstein Gyrogroups. Problems. Einstein Gyrovector Spaces. Problems. Relativistic Mass Meets Hyperbolic Geometry. Problems. Mathematical Tools for Hyperbolic Geometry. Barycentric and Gyrobarycentric Coordinates. Problems. Gyroparallelograms and Gyroparallelotopes. Problems. Gyrotrigonometry. Problems. Hyperbolic Triangles and Circles. Gyrotriangles and Gyrocircles. Problems. Gyrocircle Theorems. Problems. Hyperbolic Simplices, Hyperplanes and Hyperspheres in N Dimensions. Gyrosimplices. Problems. Gyrosimplex Gyrovolume. Problems. Hyperbolic Ellipses and Hyperbolas. Gyroellipses and Gyrohyperbolas. Problems. VI Thomas Precession. Thomas Precession. Problems. Bibliography. Index.

Abraham Albert Ungar