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| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20140310151453.0 |
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120813s2012 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783034804202 |
|
978-3-0348-0420-2 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA440-699 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
516 |
| Edition number |
23 |
| 264 #1 - |
|---|
| -- |
Basel : |
| -- |
Springer Basel : |
| -- |
Imprint: Birkhäuser, |
| -- |
2012. |
| 912 ## - |
|---|
| -- |
ZDB-2-SMA |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Benz, Walter. |
| Relator term |
author. |
| 245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
|---|
| Title |
Classical Geometries in Modern Contexts |
| Medium |
[electronic resource] : |
| Remainder of title |
Geometry of Real Inner Product Spaces Third Edition / |
| Statement of responsibility, etc |
by Walter Benz. |
| 250 ## - EDITION STATEMENT |
|---|
| Edition statement |
3rd ed. 2012. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XVII, 309 p. |
| Other physical details |
online resource. |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
Preface -- 1 Translation Groups -- 2 Euclidean and Hyperbolic Geometry -- 3 Sphere Geometries of Möbius and Lie -- 4 Lorentz Transformations -- 5 δ–Projective Mappings, Isomorphism Theorems -- 6 Planes of Leibniz, Lines of Weierstrass, Varia -- A Notation and symbols -- B Bibliography -- Index. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Geometry. |
|
|---|
| Topical term or geographic name as entry element |
Mathematical physics. |
|
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Geometry. |
|
|---|
| Topical term or geographic name as entry element |
Mathematical Methods in Physics. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
|---|
| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
|---|
| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Printed edition: |
| International Standard Book Number |
9783034804196 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-3-0348-0420-2 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
|
| Item type |
E-Book |
