双曲幾何学（第２版） Hyperbolic Geometry (Springer Undergraduate Mathematics Series (SUMS)) （2nd ed. 2005. IX, 230 p. w. 20 figs. 23,5 cm）

双曲幾何学（第２版）<br>Hyperbolic Geometry (Springer Undergraduate Mathematics Series (SUMS)) （2nd ed. 2005. IX, 230 p. w. 20 figs. 23,5 cm）

ポイントキャンペーン

双曲幾何学（第２版）
Hyperbolic Geometry (Springer Undergraduate Mathematics Series (SUMS)) （2nd ed. 2005. IX, 230 p. w. 20 figs. 23,5 cm）

Anderson, James W.

SPRINGER, BERLIN（2005発売）

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製本 Paperback:紙装版/ペーパーバック版／ページ数 230 p.
言語 ENG
商品コード 9781852339340

基本説明

Thoroughly revised and updated. Features new material and important topics such as hyperbolic geometry in higher dimensions and generalizations of hyperbolicity/ The only genuinely introductory textbook.

Full Description

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, providing the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics. Topics covered include the upper half-space model of the hyperbolic plane, Möbius transformations, the general Möbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincaré disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon 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;
a brief discussion of generalizations to higher dimensions;
many newexercises.

The Basic Spaces.- The General Möbius Group.- Length and Distance in ?.- Planar Models of the Hyperbolic Plane.- Convexity, Area, and Trigonometry.- Nonplanar models.