LEADER 03369nam 22006015 450 001 9910964617603321 005 20250730104846.0 010 $a1-4471-3987-9 024 7 $a10.1007/978-1-4471-3987-4 035 $a(CKB)2660000000025486 035 $a(SSID)ssj0000914890 035 $a(PQKBManifestationID)11508792 035 $a(PQKBTitleCode)TC0000914890 035 $a(PQKBWorkID)10864523 035 $a(PQKB)10759758 035 $a(DE-He213)978-1-4471-3987-4 035 $a(MiAaPQ)EBC3073446 035 $a(PPN)23799397X 035 $a(EXLCZ)992660000000025486 100 $a20130522d1999 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aHyperbolic Geometry /$fby James W. Anderson 205 $a1st ed. 1999. 210 1$aLondon :$cSpringer London :$cImprint: Springer,$d1999. 215 $a1 online resource (IX, 230 p.) 225 1 $aSpringer Undergraduate Mathematics Series,$x2197-4144 300 $a"With 20 Figures." 311 08$a1-85233-156-9 320 $aIncludes bibliographical references and index. 327 $a1. The Basic Spaces -- 2. The General Möbius Group -- 3. Length and Distance in ? -- 4. Other Models of the Hyperbolic Plane -- 5. Convexity, Area, and Trigonometry -- 6. Groups Acting on ? -- Solutions -- Further Reading -- References -- Notation. 330 $aThe geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, suitable for third or fourth year undergraduates. The basic approach taken is to define hyperbolic lines and develop a natural group of transformations preserving hyperbolic lines, and then study hyperbolic geometry as those quantities invariant under this group of transformations. Topics covered include the upper half-plane model of the hyperbolic plane, Möbius transformations, the general Möbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincaré disc model, convex subsets of the hyperbolic plane, hyperbolic area, the Gauss-Bonnet formula and its applications. This updated second edition also features: an expanded discussion of planar models of the hyperbolic plane arising from complex analysis; the hyperboloid model of the hyperbolic plane; brief discussion of generalizations to higher dimensions; many new exercises. The style and level of the book, which assumes few mathematical prerequisites, make it an ideal introduction to this subject and provides the reader with a firm grasp of the concepts and techniques of this beautiful part of the mathematical landscape. . 410 0$aSpringer Undergraduate Mathematics Series,$x2197-4144 606 $aGeometry 606 $aMathematics 606 $aGeometry 606 $aMathematics 615 0$aGeometry. 615 0$aMathematics. 615 14$aGeometry. 615 24$aMathematics. 676 $a516.9 700 $aAnderson$b James W$4aut$4http://id.loc.gov/vocabulary/relators/aut$0164195 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910964617603321 996 $aHyperbolic geometry$91427625 997 $aUNINA