Circles, Spheres And Spherical Geometry

[Farid-Khan]

English | 2024 | ISBN: 303162775X | 350 Pages | PDF EPUB (True) | 22 MB​

Circles, Spheres and Spherical Geometry (Hiroshi Maehara, Horst Martini) (2024)
Catergory: History, Mathematics, Nonfiction
Publisher: Springer Nature Switzerland

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.

? Contents of Download:
? 978-3-031-62776-7.epub (Hiroshi Maehara, Horst Martini) (2024) (17.84 MB)
? 978-3-031-62776-7.pdf (Glen Van Brummelen) (2012) (11.88 MB)

️ Circles, Spheres And Spherical Geometry (29.72 MB)

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