Analytic Hyperbolic Geometry

Analytic Hyperbolic Geometry
Author :
Publisher : World Scientific
Total Pages : 484
Release :
ISBN-10 : 9789812703279
ISBN-13 : 9812703276
Rating : 4/5 (79 Downloads)

Book Synopsis Analytic Hyperbolic Geometry by : Abraham A. Ungar

Download or read book Analytic Hyperbolic Geometry written by Abraham A. Ungar and published by World Scientific. This book was released on 2005 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on analytic hyperbolic geometry, fully analogous to analytic Euclidean geometry. Analytic hyperbolic geometry regulates relativistic mechanics just as analytic Euclidean geometry regulates classical mechanics. The book presents a novel gyrovector space approach to analytic hyperbolic geometry, fully analogous to the well-known vector space approach to Euclidean geometry. A gyrovector is a hyperbolic vector. In the resulting "gyrolanguage" of the book, one attaches the prefix "gyro" to a classical term to mean the analogous term in hyperbolic geometry. The book begins with the definition of gyrogroups, which is fully analogous to the definition of groups. Gyrogroups, both gyrocommutative and nongyrocommutative, abound in group theory. Surprisingly, the seemingly structureless Einstein velocity addition of special relativity turns out to be a gyrocommutative gyrogroup operation. Introducing scalar multiplication, some gyrocommutative gyrogroups of gyrovectors become gyrovector spaces. The latter, in turn, form the setting for analytic hyperbolic geometry just as vector spaces form the setting for analytic Euclidean geometry. By hybrid techniques of differential geometry and gyrovector spaces, it is shown that Einstein (Mobius) gyrovector spaces form the setting for Beltrami-Klein (Poincare) ball models of hyperbolic geometry. Finally, novel applications of Mobius gyrovector spaces in quantum computation, and of Einstein gyrovector spaces in special relativity, are presented.


Analytic Hyperbolic Geometry Related Books

Analytic Hyperbolic Geometry
Language: en
Pages: 484
Authors: Abraham A. Ungar
Categories: Mathematics
Type: BOOK - Published: 2005 - Publisher: World Scientific

DOWNLOAD EBOOK

This is the first book on analytic hyperbolic geometry, fully analogous to analytic Euclidean geometry. Analytic hyperbolic geometry regulates relativistic mech
Analytic Hyperbolic Geometry: Mathematical Foundations And Applications
Language: en
Pages: 482
Authors: Abraham Albert Ungar
Categories: Mathematics
Type: BOOK - Published: 2005-09-05 - Publisher: World Scientific

DOWNLOAD EBOOK

This is the first book on analytic hyperbolic geometry, fully analogous to analytic Euclidean geometry. Analytic hyperbolic geometry regulates relativistic mech
A Gyrovector Space Approach to Hyperbolic Geometry
Language: en
Pages: 194
Authors: Abraham Ungar
Categories: Technology & Engineering
Type: BOOK - Published: 2009-03-08 - Publisher: Morgan & Claypool Publishers

DOWNLOAD EBOOK

The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as ex
Analytic Hyperbolic Geometry And Albert Einstein's Special Theory Of Relativity (Second Edition)
Language: en
Pages: 775
Authors: Abraham Albert Ungar
Categories: Mathematics
Type: BOOK - Published: 2022-02-22 - Publisher: World Scientific

DOWNLOAD EBOOK

This book presents a powerful way to study Einstein's special theory of relativity and its underlying hyperbolic geometry in which analogies with classical resu
Essays in Mathematics and its Applications
Language: en
Pages: 659
Authors: Themistocles M. Rassias
Categories: Mathematics
Type: BOOK - Published: 2016-06-14 - Publisher: Springer

DOWNLOAD EBOOK

This volume, dedicated to the eminent mathematician Vladimir Arnold, presents a collection of research and survey papers written on a large spectrum of theories