MA 398: Geometry
Scott Taylor
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  • 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)