Circles, Spheres and Spherical Geometry - 9783031627750

Circles, Spheres and Spherical GeometryAuthor(s): Hiroshi Maehara, Horst Martini\nFormat: Hardback\nPublisher: Birkhauser Verlag AG, Switzerland\nImprint: Birkhauser Verlag AG\nISBN-13: 9783031627750, 978-3031627750\nSynopsis\nThis textbook focuses on the geometry of circles, spheres, and spherical geometry. Various classic themes are used as introductory and motivating topics.\n\nThe 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, .