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249x Filetype PDF File size 0.26 MB Source: faculty.ksu.edu.sa
P 379
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Euclidean and Non-Euclidean Geometry
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Syllabus
1. Euclidean Geometry: The Euclidean plane E2. Transformation in E2.
2 2
Theisometry group of E . Affine transformations in E . Reflections. Dilata-
tions. Rays and Angles. Affine symmetries. Triangles. Congruence theorems
for triangles. Angle sum for triangles.
2 2
2. Spherical Geometry: The sphere S . Lines of S . Distance and the tri-
2
angle inequality. Motions of S . Orthogonal transformations and Euler’s
theorem. Angles and triangles. Spherical trigonometry.
2
3. Hyperbolic Geometry: The hyperbolic plane H . M¨obius transforma-
tions. Cross ratios. The Poincar´e disk model. Angles and distances. Circles
and horocycles. Hyperbolic triangles.
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Textbooks
1. Euclidean and Non-Euclidean Geometry: An Analytic Approach, by Patrick
J. Ryan, Cambridge: Cambridge University Press (1986).
2. Modern Geometries: Non-Euclidean, Projective, and Discrete Geometry, by
Michael Henle, 2nd edition, Prentice-Hall, (2001).
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