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Instructor: Gábor Hetyei

Important information:

• Course syllabus
• Homework

Handouts:

• Study Guide for the Midterm
• Ceva's theorem
• The Fermat point
• Inversion in the complex plane
• Properties of an inversion
• Fractional linear transformations
• Fractional linear transformations that are isometries of the Poincaré disk
• Properties of an inversion
• The sensed ratio
• Trigonometric functions and complex numbers
• Connecting the two Poincaré models
• The hyperbolic Pythagorean theorem
• Sines and cosines in the Poincaré disk model of the hyperbolic plane
• The hyperbolic laws of sines and cosines for general triangles
• Lobachevsky's formula
• Hypercycles and horocycles
• Hypercycles and horocycles in the Poincaré upper half plane model
• Spherical trigonometry
• Spherical trigonometry with a simplified proof of the spherical Pythagorean theorem
• Study Guide for the Final Exam
• Spherical trigonometry formulas: you will be allowed to use these during the final exam

Useful links:

• Eric Weisstein, the creator of the on-line encyclopeda Mathworld, has a list of recommended books on Non-Euclidean geometry.
• A recommended book to complement our lecture notes is "Euclidean and Non-Euclidean Geometries: Development and History," by M. J. Greenberg.
• Inversive geometry on Wikipedia.
• Peaucellier linkage entry on Wikipedia.
• Inversion entry on Cut The Knot.