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Bücher Wissen & Bildung Englische Bücher Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie Circles, Spheres and Spherical Geometry
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Circles, Spheres and Spherical Geometry
Hiroshi Maehara, Horst Martini (Broschiert, Englisch)
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Beschreibung
This textbook focuses on the geometry of circles, spheres, and spherical geometry. Various classic 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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
11.08.2025
Sprache
Englisch
EAN
9783031627781
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Birkhäuser Advanced Texts Basler Lehrbücher
Sonderedition
Nein
Autor
Hiroshi Maehara, Horst Martini
Seitenanzahl
336
Einbandart
Broschiert
Schlagwörter
Spherical Geometry, Geodesic Segments, Spherical Polygon, Geometry of Circles and Spheres, Great Circle, Stereographic Projection, Bend Formulas, Planar Graph
Thema-Inhalt
PBM - Geometrie
PBD - Diskrete Mathematik
PBV - Kombinatorik und Graphentheorie
Höhe
235 mm
Breite
15.5 cm
Hersteller: Palgrave Macmillan, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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