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Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces Third Edition Walter Benz Author
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ISBN: 9783034804196

The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characte… Mehr…

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Classical Geometries in Modern Contexts: Geometry Of Real Inner Product Spaces - neues Buch

ISBN: 9783034804196

The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characte… Mehr…

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Benz, Walter:
Classical Geometries in Modern Contexts - gebunden oder broschiert

2012

ISBN: 9783034804196

Erscheinungsdatum: 13.08.2012, Medium: Buch, Einband: Gebunden, Titel: Classical Geometries in Modern Contexts, Titelzusatz: Geometry of Real Inner Product Spaces Third Edition, Auflage: … Mehr…

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ISBN: 9783034804196

Hardback, [PU: Springer Basel], This book explores real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. The third editi… Mehr…

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Walter Benz:
Classical Geometries in Modern Contexts - gebunden oder broschiert

2012, ISBN: 9783034804196

Geometry of Real Inner Product Spaces Third Edition, [ED: 3], 3rd ed. 2012, Hardcover, Buch, [PU: Springer Basel]

Versandkosten:Versand in 10-20 Tagen, , Spedizione gratuita in Germania. (EUR 9.95)


Details zum Buch
Classical Geometries in Modern Contexts

The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characterizes both euclidean and hyperbolic geometry with respect to natural properties of (general) translations and general distances of X. Also for these spaces X, it studies the sphere geometries of Möbius and Lie as well as geometries where Lorentz transformations play the key role.

Proofs of newer theorems characterizing isometries and Lorentz transformations under mild hypotheses are included, such as for instance infinite dimensional versions of famous theorems of A.D. Alexandrov on Lorentz transformations. A real benefit is the dimension-free approach to important geometrical theories.

New to this third edition is a chapter dealing with a simple and great idea of Leibniz that allows us to characterize, for these same spaces X, hyperplanes of euclidean, hyperbolic geometry, or spherical geometry, the geometries of Lorentz-Minkowski and de Sitter, and this through finite or infinite dimensions greater than 1.

Another new and fundamental result in this edition concerns the representation of hyperbolic motions, their form and their transformations. Further we show that the geometry (P,G) of segments based on X is isomorphic to the hyperbolic geometry over X. Here P collects all x in X of norm less than one, G is defined to be the group of bijections of P transforming segments of P onto segments.

The only prerequisites for reading this book are basic linear algebra and basic 2- and 3-dimensional real geometry. This implies that mathematicians who have not so far been especially interested in geometry could study and understand some of the great ideas of classical geometries in modern and general contexts.

Detailangaben zum Buch - Classical Geometries in Modern Contexts


EAN (ISBN-13): 9783034804196
ISBN (ISBN-10): 3034804199
Gebundene Ausgabe
Erscheinungsjahr: 2012
Herausgeber: Springer Basel
309 Seiten
Gewicht: 0,624 kg
Sprache: Englisch

Buch in der Datenbank seit 2007-05-30T05:23:40+02:00 (Berlin)
Detailseite zuletzt geändert am 2020-07-11T18:36:44+02:00 (Berlin)
ISBN/EAN: 9783034804196

ISBN - alternative Schreibweisen:
3-0348-0419-9, 978-3-0348-0419-6


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