E Book

Hyperbolic Geometry

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The Basic Spaces -- The General Möbius Group -- Length and Distance in ? -- Planar Models of the Hyperbolic Plane -- Convexity, Area, and Trigonometry -- Nonplanar models.The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, suitable for third or fourth year undergraduates. The basic approach taken is to define hyperbolic lines and develop a natural group of transformations preserving hyperbolic lines, and then study hyperbolic geometry as those quantities invariant under this group of transformations. Topics covered include the upper half-plane model of the hyperbolic plane, Möbius transformations, the general Möbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincaré disc model, convex subsets of the hyperbolic plane, hyperbolic area, the Gauss-Bonnet formula and its applications. This updated second edition also features: an expanded discussion of planar models of the hyperbolic plane arising from complex analysis; the hyperboloid model of the hyperbolic plane; brief discussion of generalizations to higher dimensions; many new exercises. The style and level of the book, which assumes few mathematical prerequisites, make it an ideal introduction to this subject and provides the reader with a firm grasp of the concepts and techniques of this beautiful part of the mathematical landscape. .

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Ketersediaan

Informasi Detail

Judul Seri

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No. Panggil

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Penerbit

London : Springer., 2005

Deskripsi Fisik

XII, 276 p. 21 illus.online resource.

Bahasa

English

ISBN/ISSN

9781846282201

Klasifikasi

516

Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

2nd ed. 2005.

Subjek

Mathematics.
Mathematics, general.
Geometry.

Info Detail Spesifik

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Pernyataan Tanggungjawab

James W. Anderson.

Versi lain/terkait

Lampiran Berkas

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