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lgli/290.pdf
Classical geometries in modern contexts : geometry of real inner product spaces Walter Benz Birkhauser Basel, Boston, Mass, Massachusetts, 2005
<p><P>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 M&ouml;bius 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. <P>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&ndash;free approach to important geometrical theories. Only prerequisites are basic linear algebra and basic 2&ndash; and 3&ndash;dimensional real geometry.<P></p>
更多信息……
英语 [en] · PDF · 2.3MB · 2005 · 📘 非小说类图书 · 🚀/lgli/lgrs · Save
base score: 11065.0, final score: 17462.576
nexusstc/Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces/51f6cc7af38838aa771514246e0ef06b.pdf
Classical geometries in modern contexts : geometry of real inner product spaces Walter Benz, 1931- Birkhäuser Basel, 1, 2005
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.
更多信息……
英语 [en] · PDF · 1.6MB · 2005 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/zlib · Save
base score: 11065.0, final score: 17460.225
lgli/D:\!genesis\library.nu\ff\_172729.ffe1ef84262fe7671a088424d7951d77.pdf
Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces, 1st Edition Walter Benz, 1931- Birkhäuser Basel, 1, 2005
<p><P>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 M&ouml;bius 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. <P>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&ndash;free approach to important geometrical theories. Only prerequisites are basic linear algebra and basic 2&ndash; and 3&ndash;dimensional real geometry.<P></p>
更多信息……
英语 [en] · PDF · 1.5MB · 2005 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/zlib · Save
base score: 11065.0, final score: 17460.217
lgli/D:\!genesis\library.nu\d7\_48064.d7866938eb3dacb3419b418bed058a46.pdf
Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces, 1st Edition Walter Benz, 1931- Birkhäuser Basel, 1, 2005
<p><P>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 M&ouml;bius 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. <P>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&ndash;free approach to important geometrical theories. Only prerequisites are basic linear algebra and basic 2&ndash; and 3&ndash;dimensional real geometry.<P></p>
更多信息……
英语 [en] · PDF · 1.8MB · 2005 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/zlib · Save
base score: 11065.0, final score: 17460.113
lgli/M_Mathematics/MD_Geometry and topology/Benz W. Classical Geometries in Modern Contexts.. Geometry of Real Inner Product Spaces (ISBN 3764373717)(Springer, 2005)(251s)_MD_.pdf
Classical geometries in modern contexts : geometry of real inner product spaces Walter Benz, 1931- Birkhäuser Basel, 1, 2005
<p><P>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 M&ouml;bius 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. <P>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&ndash;free approach to important geometrical theories. Only prerequisites are basic linear algebra and basic 2&ndash; and 3&ndash;dimensional real geometry.<P></p>
更多信息……
英语 [en] · PDF · 1.6MB · 2005 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/zlib · Save
base score: 11065.0, final score: 17459.818
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