Hyperbolic Geometry

TRAMA

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.

SOMMARIO

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

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9781852339340
• Collana: Springer Undergraduate Mathematics Series
• Dimensioni: 254 x 178 mm
• Formato: Brossura
• Illustration Notes: XII, 276 p. 21 illus.
• Pagine Arabe: 276
• Pagine Romane: xii