Mathematics 138 - Classical Geometry; Fall 2000

Instructor: Danny Calegari 432 Science Center

Course Assistant: Kathy Paur 321b Science Center

Description of course

An introduction to spherical, Euclidean and hyperbolic geometry in two and three dimensions, with an emphasis on the similarities and differences between these flavors of geometry. The most important tool in analyzing these geometries will be a study of their symmetries; we will see how this leads naturally to basic notions in group theory and topology. Topics to be covered might include classical tessellations, the Gauss-Bonnet theorem, scissors congruence, orbifolds, and fibered geometries.

Available for download

Answers to homework problems should take the form of complete sentences. It's important not merely to find the solution to a problem, but also to communicate that solution effectively.

The final exam was posted on this webpage at noon on Thursday the 4th of January.

Recommended texts for course

Useful for extra reading

last updated: 22nd December 2000

If you have any comments on the material in this page, or if you wish to comment on the material in the course, contact Danny Calegari via email

The image to the right is Heaven and Hell (Circle limit IV) by Maurits C. Escher, the well-known 20th century Dutch artist. It depicts a tessellation of the hyperbolic plane by two kinds of tiles, angels and devils. The model of the hyperbolic plane used is the Poincaré (or conformal) model.

Danny Calegari's home page