| 000 | 04072nam a22005655i 4500 | ||
|---|---|---|---|
| 001 | 978-3-031-62776-7 | ||
| 003 | DE-He213 | ||
| 005 | 20251030112847.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 240810s2024 sz | s |||| 0|eng d | ||
| 020 |
_a9783031627767 _9978-3-031-62776-7 |
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| 024 | 7 |
_a10.1007/978-3-031-62776-7 _2doi |
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| 050 | 4 | _aQA440-699 | |
| 072 | 7 |
_aPBM _2bicssc |
|
| 072 | 7 |
_aMAT012000 _2bisacsh |
|
| 072 | 7 |
_aPBM _2thema |
|
| 100 | 1 |
_aMaehara, Hiroshi. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _982169 |
|
| 245 | 1 | 0 |
_aCircles, Spheres and Spherical Geometry _h[electronic resource] / _cby Hiroshi Maehara, Horst Martini. |
| 250 | _a1st ed. 2024. | ||
| 264 | 1 |
_aCham : _bSpringer Nature Switzerland : _bImprint: Birkhäuser, _c2024. |
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| 300 |
_aXIV, 336 p. 85 illus., 1 illus. in color. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
||
| 490 | 1 |
_aBirkhäuser Advanced Texts Basler Lehrbücher, _x2296-4894 |
|
| 505 | 0 | _a- Inversion and stereographic projection -- Bend formulas -- Graphs and circle-systems -- Spherical geometry I -- Spherical geometry II -- The problem of thirteen balls -- Spherical geometry III -- Geometric probability on the sphere -- Intersection graphs of spherical caps -- Quartets on a sphere -- Higher dimensions -- The Cayley-Menger determinant -- Casey's theorem -- Solutions to the selected exercises. | |
| 520 | _aThis textbook focuses on the geometry of circles, spheres, and spherical geometry. Various classical themes are used as introductory and motivating topics. The book begins very simply for the reader in the first chapter discussing the notions of inversion and stereographic projection. Here, various classical topics and theorems such as Steiner cycles, inversion, Soddy's hexlet, stereographic projection and Poncelet's porism are discussed. The book then delves into Bend formulas and the relation of radii of circles, focusing on Steiner circles, mutually tangent four circles in the plane and other related notions. Next, some fundamental concepts of graph theory are explained. The book then proceeds to explore orthogonal-cycle representation of quadrangulations, giving detailed discussions of the Brightwell-Scheinerman theorem (an extension of the Koebe-Andreev-Thurston theorem), Newton’s 13-balls-problem, Casey’s theorem (an extension of Ptolemy’s theorem) and its generalizations. The remainder of the book is devoted to spherical geometry including a chapter focusing on geometric probability on the sphere. The book also contains new results of the authors and insightful notes on the existing literature, bringing the reader closer to the research front. Each chapter concludes with related exercises of varying levels of difficulty. Solutions to selected exercises are provided. This book is suitable to be used as textbook for a geometry course or alternatively as basis for a seminar for both advanced undergraduate and graduate students alike. | ||
| 650 | 0 |
_aGeometry. _968763 |
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| 650 | 0 |
_aConvex geometry . _971929 |
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| 650 | 0 |
_aDiscrete geometry. _971930 |
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| 650 | 0 | _aGraph theory. | |
| 650 | 1 | 4 |
_aGeometry. _968763 |
| 650 | 2 | 4 |
_aConvex and Discrete Geometry. _971931 |
| 650 | 2 | 4 | _aGraph Theory. |
| 700 | 1 |
_aMartini, Horst. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _980552 |
|
| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer Nature eBook | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031627750 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031627774 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031627781 |
| 830 | 0 |
_aBirkhäuser Advanced Texts Basler Lehrbücher, _x2296-4894 _980556 |
|
| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-031-62776-7 |
| 912 | _aZDB-2-SMA | ||
| 912 | _aZDB-2-SXMS | ||
| 999 |
_c62374 _d62374 |
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