Analytic hyperbolic geometry : mathematical foundations and applications / Abraham A. Ungar.

Format:

Book

Author/Creator:

Ungar, Abraham A.

Language:

English

Subjects (All):

Geometry, Hyperbolic--Textbooks.

Geometry, Hyperbolic.

Vector algebra--Textbooks.

Vector algebra.

Physical Description:

1 online resource (482 p.)

Edition:

1st ed.

Place of Publication:

New Jersey : World Scientific, c2005.

Language Note:

English

Summary:

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. Gyrovectors are equivalence classes of directed gyrosegments that add according to the gyroparallelogram law just as vectors are equivalence classes of directed segme

Contents:

Preface; Acknowledgements; Contents; 1. Introduction; 2. Gyrogroups; 3. Gyrocommutative Gyrogroups; 4. Gyrogroup Extension; 5. Gyrovectors and Cogyrovectors; 6. Gyrovector Spaces; 7. Rudiments of Differential Geometry; 8. Gyrotrigonometry; 9. Bloch Gyrovector of Quantum Computation; 10. Special Theory of Relativity: The Analytic Hyperbolic Geometric Viewpoint; Notation And Special Symbols; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 445-456) and index.

ISBN:

9786611899226

9781281899224

1281899224

9789812703279

9812703276

OCLC:

228171823