| 书目名称 | Circles, Spheres and Spherical Geometry | | 编辑 | Hiroshi Maehara,Horst Martini | | 视频video | http://file.papertrans.cn/243/242124/242124.mp4 | | 概述 | Presents cross-connections of geometry of circles and spherical geometry from various points of view.Motivates readers to derive own new results.Includes solutions to selected exercises | | 丛书名称 | Birkhäuser Advanced Texts‘ Basler Lehrbücher | | 图书封面 |  | | 描述 | .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 | | 出版日期 | Textbook 2024 | | 关键词 | Spherical Geometry; Geodesic Segments; Spherical Polygon; Geometry of Circles and Spheres; Great Circle; | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-62776-7 | | isbn_softcover | 978-3-031-62778-1 | | isbn_ebook | 978-3-031-62776-7Series ISSN 1019-6242 Series E-ISSN 2296-4894 | | issn_series | 1019-6242 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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