Overview

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.

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9781482236675

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Anyone who is concerned with hyperbolic geometry should use this wonderful and comprehensive book as a helpful compendium. -Zentralblatt MATH 1312

Anyone who is concerned with hyperbolic geometry should use this wonderful and comprehensive book as helpful compendium. Readers of the book should have a basic knowledge of linear algebra and Euclidean geometry, but no 'prior acquaintance with either hyperbolic geometry, special relativity, or nonassociative algebra' is required. Because of many complicated algebraic manipulations computer algebra is indispensable. -Rolf Riesinger, in Zentralblatt MATH

Author Information

Abraham Albert Ungar

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