ARCHIVE PAGE

Instructor: Gábor Hetyei

Important information:

• Course syllabus
• Homework
• Study guide to the midterm exam.
• Study guide to the (mandatory part of the) final exam.

Our Final Exam will be on Monday May 7, 5:00-7:30 PM. You may dowload a the study guide I distributed on Monday April 30.

Handouts:

• Ceva's theorem
• The Fermat point
• The sensed ratio
• The crossbar theorem (with corrected proof)
• Inversion in the complex plane
• Properties of an inverson
• The hyperbolic Pythagorean theorem (perliminary version)
• Fractional linear transformations
• Connecting the two Poincaré models
• Sines and cosines in the Poincaré disk model of the hyperbolic plane
• The hyperbolic laws of sines and cosines for general triangles
• The spherical Pythagorean theorem
• Hypercycles and horocycles in the Poincaré upper half plane model

External links:

• Professor Royster, the author of our text, has homepages for his past MATH 6118 courses online: the Spring 2002 page, the Spring 2004 page and the Spring 2008 page contain downloadable excerpts of our lecture notes (out of date compared to what you find in the bookstore!), exercises and links to further webpages with relevant information.
• 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.
• Real Projective Plane on Wikipedia.
• Cross Ratio entry on Cut The Knot.
• Inversive geometry on Wikipedia.
• Peaucellier linkage entry on Wikipedia.
• Inversion entry on Cut The Knot.
• Poincaré disk model entry on Wikipedia.
• Poincaré disk model entry on Mathworld.
• Murray's Spherical Trigonometry on archive.org.