03864nam a22005175i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001600186072002300202072001500225100008600240245010500326250001800431264007300449300006400522336002600586337002600612338003600638347002400674490006400698505041600762520157401178650002102752650003002773650003002803650001802833650002102851650004102872650001802913700008402931710003403015773002603049776003603075776003603111776003603147830007103183856004603254912001403300912001503314999001703329978-3-031-62776-7DE-He21320251030112847.0cr nn 008mamaa240810s2024    sz |    s    |||| 0|eng d  a97830316277679978-3-031-62776-77 a10.1007/978-3-031-62776-72doi 4aQA440-699 7aPBM2bicssc 7aMAT0120002bisacsh 7aPBM2thema1 aMaehara, Hiroshi.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98216910aCircles, Spheres and Spherical Geometryh[electronic resource] /cby Hiroshi Maehara, Horst Martini.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Birkhäuser,c2024.  aXIV, 336 p. 85 illus., 1 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aBirkhäuser Advanced Texts Basler Lehrbücher,x2296-48940 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.  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. 0aGeometry.968763 0aConvex geometry .971929 0aDiscrete geometry.971930 0aGraph theory.14aGeometry.96876324aConvex and Discrete Geometry.97193124aGraph Theory.1 aMartini, Horst.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9805522 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303162775008iPrinted edition:z978303162777408iPrinted edition:z9783031627781 0aBirkhäuser Advanced Texts Basler Lehrbücher,x2296-489498055640uhttps://doi.org/10.1007/978-3-031-62776-7  aZDB-2-SMA  aZDB-2-SXMS  c62374d62374