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Autor Walter Benz |
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Título : Classical Geometries in Modern Contexts : Geometry of Real Inner Product Spaces Tipo de documento: documento electrónico Autores: Walter Benz ; SpringerLink (Online service) Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2005 Número de páginas: XII, 244 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-7432-7 Idioma : Inglés (eng) Palabras clave: Mathematics Geometry Physics Mathematical Methods in Clasificación: 51 Matemáticas Resumen: 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 geometries of Möbius and Lie are studied (besides euclidean and hyperbolic geometry), as well as geometries where Lorentz transformations play the key role. 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. Proofs of newer theorems, characterizing isometries and Lorentz transformations under mild hypotheses are included, like 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. Only prerequisites are basic linear algebra and basic 2- and 3-dimensional real geometry Nota de contenido: Translation Groups -- Euclidean and Hyperbolic Geometry -- Sphere Geometries of Möbius and Lie -- Lorentz Transformations En línea: http://dx.doi.org/10.1007/3-7643-7432-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35348 Classical Geometries in Modern Contexts : Geometry of Real Inner Product Spaces [documento electrónico] / Walter Benz ; SpringerLink (Online service) . - Basel : Birkhäuser Basel, 2005 . - XII, 244 p : online resource.
ISBN : 978-3-7643-7432-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Geometry Physics Mathematical Methods in Clasificación: 51 Matemáticas Resumen: 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 geometries of Möbius and Lie are studied (besides euclidean and hyperbolic geometry), as well as geometries where Lorentz transformations play the key role. 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. Proofs of newer theorems, characterizing isometries and Lorentz transformations under mild hypotheses are included, like 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. Only prerequisites are basic linear algebra and basic 2- and 3-dimensional real geometry Nota de contenido: Translation Groups -- Euclidean and Hyperbolic Geometry -- Sphere Geometries of Möbius and Lie -- Lorentz Transformations En línea: http://dx.doi.org/10.1007/3-7643-7432-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35348 Ejemplares
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Título : Classical Geometries in Modern Contexts : Geometry of Real Inner Product Spaces Tipo de documento: documento electrónico Autores: Walter Benz ; SpringerLink (Online service) Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2007 Número de páginas: XII, 277 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8541-5 Idioma : Inglés (eng) Palabras clave: Mathematics Geometry Physics Mathematical Methods in Clasificación: 51 Matemáticas Resumen: 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 geometries of Möbius and Lie are studied (besides euclidean and hyperbolic geometry), as well as geometries where Lorentz transformations play the key role. 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. Proofs of newer theorems, characterizing isometries and Lorentz transformations under mild hypotheses are included, like 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. Only prerequisites are basic linear algebra and basic 2- and 3-dimensional real geometry Nota de contenido: Translation Groups -- Euclidean and Hyperbolic Geometry -- Sphere Geometries of Möbius and Lie -- Lorentz Transformations -- ?-Projective Mappings, Isomorphism Theorems En línea: http://dx.doi.org/10.1007/978-3-7643-8541-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34722 Classical Geometries in Modern Contexts : Geometry of Real Inner Product Spaces [documento electrónico] / Walter Benz ; SpringerLink (Online service) . - Basel : Birkhäuser Basel, 2007 . - XII, 277 p : online resource.
ISBN : 978-3-7643-8541-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Geometry Physics Mathematical Methods in Clasificación: 51 Matemáticas Resumen: 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 geometries of Möbius and Lie are studied (besides euclidean and hyperbolic geometry), as well as geometries where Lorentz transformations play the key role. 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. Proofs of newer theorems, characterizing isometries and Lorentz transformations under mild hypotheses are included, like 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. Only prerequisites are basic linear algebra and basic 2- and 3-dimensional real geometry Nota de contenido: Translation Groups -- Euclidean and Hyperbolic Geometry -- Sphere Geometries of Möbius and Lie -- Lorentz Transformations -- ?-Projective Mappings, Isomorphism Theorems En línea: http://dx.doi.org/10.1007/978-3-7643-8541-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34722 Ejemplares
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Título : Classical Geometries in Modern Contexts : Geometry of Real Inner Product Spaces Third Edition Tipo de documento: documento electrónico Autores: Walter Benz ; SpringerLink (Online service) Editorial: Basel : Springer Basel Fecha de publicación: 2012 Otro editor: Imprint: Birkhäuser Número de páginas: XVIII, 310 p Il.: online resource ISBN/ISSN/DL: 978-3-0348-0420-2 Idioma : Inglés (eng) Palabras clave: Mathematics Geometry Physics Mathematical Methods in Clasificación: 51 Matemáticas Resumen: 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 Nota de contenido: Preface -- 1 Translation Groups -- 2 Euclidean and Hyperbolic Geometry -- 3 Sphere Geometries of Möbius and Lie -- 4 Lorentz Transformations -- 5 d–Projective Mappings, Isomorphism Theorems -- 6 Planes of Leibniz, Lines of Weierstrass, Varia -- A Notation and symbols -- B Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0420-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32891 Classical Geometries in Modern Contexts : Geometry of Real Inner Product Spaces Third Edition [documento electrónico] / Walter Benz ; SpringerLink (Online service) . - Basel : Springer Basel : Imprint: Birkhäuser, 2012 . - XVIII, 310 p : online resource.
ISBN : 978-3-0348-0420-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Geometry Physics Mathematical Methods in Clasificación: 51 Matemáticas Resumen: 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 Nota de contenido: Preface -- 1 Translation Groups -- 2 Euclidean and Hyperbolic Geometry -- 3 Sphere Geometries of Möbius and Lie -- 4 Lorentz Transformations -- 5 d–Projective Mappings, Isomorphism Theorems -- 6 Planes of Leibniz, Lines of Weierstrass, Varia -- A Notation and symbols -- B Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0420-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32891 Ejemplares
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