The Poincaré Half-plane: A Gateway to Modern GeometryJones & Bartlett Learning, 1993 - 298 σελίδες The Poincare Half-Planeprovides an elementary and constructive development of this geometry that brings the undergraduate major closer to current geometric research. At the same time, repeated use is made of high school geometry, algebra, trigonometry, and calculus, thus reinforcing the students' understanding of these disciplines as well as enhancing their perception of mathematics as a unified endeavor. |
Περιεχόμενα
EUCLIDEAN RIGID MOTIONS | 35 |
INVERSIONS | 51 |
THE HYPERBOLIC PLANE | 63 |
EUCLIDEAN VERSUS HYPERBOLIC GEOMETRY | 79 |
THE ANGLES OF THE HYPERBOLIC TRIANGLE | 93 |
HYPERBOLIC AREA | 109 |
THE TRIGONOMETRY OF THE HYPERBOLIC | 119 |
The general hyperbolic triangle | 125 |
SPHERICAL TRIGONOMETRY AND ELLIPTIC | 167 |
DIFFERENTIAL GEOMETRY AND GAUSSIAN | 183 |
THE CROSS RATIO AND THE UNIT DISK | 207 |
Explicit rigid motions of the unit disk model | 221 |
Regular tesselations of the unit disk model | 228 |
A BRIEF HISTORY OF NONEUCLIDEAN | 247 |
Exercises | 254 |
APPPENDIX | 277 |
COMPLEX NUMBERS AND RIGID MOTIONS | 131 |
ABSOLUTE GEOMETRY AND THE ANGLES | 161 |
BIBLIOGRAPHY | 293 |
Συχνά εμφανιζόμενοι όροι και φράσεις
absolute geometry arbitrary arcs axioms axis Beltrami-Klein Beltrami-Klein model bowed geodesic Chapter Common Notions complex numbers composition congruent containing cos² cosh cross ratio curvature curve defined denote dx² dy² elliptic elliptic geometry equation Euclidean center Euclidean circle Euclidean geometry Euclidean plane Euclidean straight lines Example Exercise FIGURE fixed point flow diagram flow lines follows function Gauss Gaussian curvature geodesic segment given glide-reflections Hence hyperbolic area hyperbolic distance hyperbolic geometry hyperbolic length hyperbolic plane hyperbolic reflection hyperbolic rigid motion hyperbolic rotation hyperbolic triangle interior intersect inversion Lemma mathematicians Moebius rigid motion Moebius transformation non-Euclidean geometry parallel Parallel Postulate Poincaré metric proof of Proposition Prove reader Riemann metric right angles sides sin² sinh sphere straight geodesic surface tangent Theorem translation triangle ABC unit disk model upper half-plane vertices x-axis xy plane მუ
Αναφορές για αυτό το βιβλίο
Mathematical Expeditions: Chronicles by the Explorers Reinhard Laubenbacher,David Pengelley Περιορισμένη προεπισκόπηση - 2000 |