| 000 | 02946nam a22004695i 4500 | ||
|---|---|---|---|
| 001 | 978-3-7643-8541-5 | ||
| 003 | DE-He213 | ||
| 005 | 20181204132645.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 100301s2007 sz | s |||| 0|eng d | ||
| 020 |
_a9783764385415 _9978-3-7643-8541-5 |
||
| 024 | 7 |
_a10.1007/978-3-7643-8541-5 _2doi |
|
| 040 | _aISI Library, Kolkata | ||
| 050 | 4 | _aQA440-699 | |
| 072 | 7 |
_aPBM _2bicssc |
|
| 072 | 7 |
_aMAT012000 _2bisacsh |
|
| 072 | 7 |
_aPBM _2thema |
|
| 082 | 0 | 4 |
_a516 _223 |
| 100 | 1 |
_aBenz, Walter. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
| 245 | 1 | 0 |
_aClassical Geometries in Modern Contexts _h[electronic resource] : _bGeometry of Real Inner Product Spaces / _cby Walter Benz. |
| 250 | _aSecond Edition. | ||
| 264 | 1 |
_aBasel : _bBirkhäuser Basel, _c2007. |
|
| 300 |
_aXII, 277 p. _bonline resource. |
||
| 336 |
_atext _btxt _2rdacontent |
||
| 337 |
_acomputer _bc _2rdamedia |
||
| 338 |
_aonline resource _bcr _2rdacarrier |
||
| 347 |
_atext file _bPDF _2rda |
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| 505 | 0 | _aTranslation Groups -- Euclidean and Hyperbolic Geometry -- Sphere Geometries of Möbius and Lie -- Lorentz Transformations -- ?-Projective Mappings, Isomorphism Theorems. | |
| 520 | _aThis 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. | ||
| 650 | 0 | _aGeometry. | |
| 650 | 0 | _aMathematical physics. | |
| 650 | 1 | 4 |
_aGeometry. _0http://scigraph.springernature.com/things/product-market-codes/M21006 |
| 650 | 2 | 4 |
_aMathematical Methods in Physics. _0http://scigraph.springernature.com/things/product-market-codes/P19013 |
| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer eBooks | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783764392222 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783764385408 |
| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-7643-8541-5 |
| 912 | _aZDB-2-SMA | ||
| 942 | _cEB | ||
| 950 | _aMathematics and Statistics (Springer-11649) | ||
| 999 |
_c425556 _d425556 |
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