Circles, Spheres and Spherical Geometry

Name: Circles, Spheres and Spherical Geometry
Brand: Springer, Berlin
SKU: 9783031627750
Price: 1566 CZK
Availability: InStock

Autor: Hiroshi Maehara, Horst Martini

Jazyk:

Vazba: Pevná

Vydavatel: Springer, Berlin

Dostupnost: Skladem u dodavatele

Odesíláme za 10-13 dnů

1 566 Kč

This textbook focuses on the geometry of circles, spheres, and spherical geometry. Various classic t...

Informace o knize

Autor

Hiroshi Maehara, Horst Martini

Jazyk

Angličtina

Vazba

Kniha - Pevná

Vydáno

2024

Stránek

436

EAN

9783031627750

Enbook ID

46025581

Vydavatel

Springer, Berlin

Hmotnost

637

Rozměry

155 x 235

Kompletní popis

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.

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Circles, Spheres and Spherical Geometry

Informace o knize

Kompletní popis

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