Name: Circles, Spheres and Spherical Geometry
Price: 67.23 EUR
Availability: InStock
Author: Hiroshi Maehara;Horst Martini
ISBN: 9783031627781

portada Circles, Spheres and Spherical Geometry

Type

Physical Book

Publisher

Birkhauser Verlag AG

Author

Hiroshi Maehara;Horst Martini

Collection

Birkhauser Advanced Texts Basler Lehrbucher

Year

2025

Pages

336

Format

Paperback

Dimensions

23.50 x 15.50 cm

ISBN13

9783031627781

Circles, Spheres and Spherical Geometry

Hiroshi Maehara;Horst Martini (Author) · Birkhauser Verlag AG · Paperback

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Synopsis "Circles, Spheres and Spherical Geometry"

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.