- Paths in Euclidean Space
This handout proves that in euclidean space a straight line is the shortest path between two points and that the path metric for subsets of euclidean space is a metric.
- Sup Metric and Euclidean Metric
This handout proves that the identity map from R^2 with the euclidean metric to R^2 with the sup metric is a homeomorphism.
- The Grasshopper Metric
This handout proves that the grasshopper metric on the surface arising from gluing edges of a euclidean polygon is well-behaved.
- The Figure 8 knot complement
These slides show how to decompose the figure 8 knot complement into two tetrahedra with their vertices removed.
- Special Relativity and Hyperbolic Geometry
These slides give some idea of the relationship between special relativity and hyperbolic geometry. (Based on a book by Woodhouse)
- Trees and Hyperbolic Geometry
These slides show how a problem from computer science can be solved using hyperbolic geometry. (Based on a paper of Sleator, Tarjan, and Thurston)