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# Classical Geometries in Modern Contexts Geometry of Real.

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. About this book. 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. This book is based on real inner product spaces X of arbitrary finite or infinite dimension greater than or equal to 2. With natural properties of general translations and general distances of X, euclidean and hyperbolic geometries are characterized. For these spaces X also the sphere.

Walter Benz, "Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces Third Edition" English ISBN: 3034804199 2012 328 pages PDF 2 MB 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. Mar 21, 2019 · Classical Geometries in Modern Contexts Geometry of Real Inner Product Spaces 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. Classical geometries in modern contexts: geometry of real inner product spaces. [Walter Benz] -- 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. Your Web browser is not enabled for JavaScript.

Introduction. 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. Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces Third Edition. 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. Walter Benz 2007 Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces, chapter 3: Sphere geometries of Möbius and Lie, pages 93–174, Birkhäuser, ISBN 978-3. May 01, 2009 · They are all orthogonal to the line through a and s. References [1] W. Benz, Classical Geometries in Modern Contexts. Geometry of Real Inner Product Spaces, Birkh¨ auser Publ. Comp., Basel, Boston, Berlin. First edition, 2005, second and enlarged edition, 2007. [2] W. Classical geometries in modern contexts: geometry of real inner product spaces. [Walter Benz] -- "This book is based on real inner product spaces X of arbitrary finite or infinite dimension greater than or equal to 2.

The geometrical notions of this book are based on general spaces X as described. This implies that also mathematicians who have not so far been especially interested in geometry may study and understand great ideas of classical geometries in modern and general contexts. Classical Geometries in Modern Contexts Geometry of Real Inner Product Spaces Third Edition 3rd Edition by Walter Benz and Publisher Birkhäuser. Save up to 80% by choosing the eTextbook option for ISBN: 9783034804202, 3034804202.

## Classical Geometries in Modern Contexts SpringerLink.

This book is based on real inner product spaces X of arbitrary finite or infinite dimension greater than or equal to 2. Designed as a two term graduate course, the book helps students to understand great ideas of classical geometries in a modern and general context. A real benefit is the dimension-free approach to important geometrical theories.