Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces - Couverture rigide

Benz, Walter

9783034804196: Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces

Couverture rigide

ISBN 10 : 3034804199 ISBN 13 : 9783034804196

Editeur : Birkhauser Verlag AG, 2012

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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 edition includes new insight into a simple idea of Liebniz, new representation of hyperbolic motions and more.

Les informations fournies dans la section � Synopsis � peuvent faire r�f�rence � une autre �dition de ce titre.

�diteurBirkhauser Verlag AG
Date d'�dition2012
ISBN 10 3034804199
ISBN 13 9783034804196
ReliureReli�
Langueanglais
Num�ro d'�dition3
Nombre de pages310
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9783034807418: Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces Third Edition

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ISBN 10 : 3034807414 ISBN 13 : 9783034807418
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Classical Geometries in Modern Contexts

Walter Benz

Edit� par Springer Basel, 2012

ISBN 10 : 3034804199 ISBN 13 : 9783034804196

Neuf Couverture rigide

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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Dimension-free presentation Inclusion of proofs of newer theorems characterizing isometries and Lorentz transformations under mild hypothesesCommon presentation for finite and infinite dimensional real inner product spaces X on an elementary basis, i.e., av. N� de r�f. du vendeur 4318238

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Classical Geometries in Modern Contexts : Geometry of Real Inner Product Spaces Third Edition

Walter Benz

Edit� par Springer Basel, 2012

ISBN 10 : 3034804199 ISBN 13 : 9783034804196

Neuf Couverture rigide

Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne

�valuation du vendeur 5 sur 5 �toiles

Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 M�bius 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. N� de r�f. du vendeur 9783034804196

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Classical Geometries in Modern Contexts

Walter Benz

Edit� par Springer Basel Aug 2012, 2012

ISBN 10 : 3034804199 ISBN 13 : 9783034804196

Neuf Couverture rigide

impression � la demande

Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne

�valuation du vendeur 5 sur 5 �toiles

Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 M�bius 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. 328 pp. Englisch. N� de r�f. du vendeur 9783034804196

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Classical Geometries in Modern Contexts

Walter Benz

Edit� par Springer Basel, Birkh�user Basel Aug 2012, 2012

ISBN 10 : 3034804199 ISBN 13 : 9783034804196

Neuf Couverture rigide

Vendeur : buchversandmimpf2000, Emtmannsberg, BAYE, Allemagne

�valuation du vendeur 5 sur 5 �toiles

Buch. Etat : Neu. Neuware -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 M�bius 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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 328 pp. Englisch. N� de r�f. du vendeur 9783034804196

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