The Poincaré Half-plane: A Gateway to Modern Geometry

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Jones & Bartlett Learning, 1993 - 298 Seiten
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.
 

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Inhalt

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
A review of lengths and areas on surfaces
190
Gausss formula for the curvature at a point
196
Exercises
205
The unit disk model and its flow diagrams
213
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

COMPLEX NUMBERS AND RIGID MOTIONS
131
ABSOLUTE GEOMETRY AND THE ANGLES
161
SPHERICAL TRIGONOMETRY AND ELLIPTIC
167
DIFFERENTIAL GEOMETRY AND GAUSSIAN
183
APPPENDIX
277
BIBLIOGRAPHY
293
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