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OverviewThis 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. Full Product DetailsAuthor: Abraham A UngarPublisher: World Scientific Publishing Company Imprint: World Scientific Publishing Company ISBN: 9781281899224ISBN 10: 1281899224 Pages: 463 Publication Date: 01 January 2005 Audience: General/trade , General Format: Electronic book text Publisher's Status: Active Availability: In stock We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |