February 14

Plan:

- Questions
- Crochet, tiling, … play in the hyperbolic plane
- Riemannian geometry
- On to Chapter 2

Student Questions:

- Would like more clarification on homework questions, perhaps visual demonstration. I have read a couple of online articles posted here as well as
*Mathematical Expeditions*but still feel like I could benefit from some additional elucidation. —Rob Moray

Discussion

The discussion page can be found here

- Tiling
- Definitions, examples: [http://www.math.cornell.edu/~mec/Winter2009/Mihai/section9.html]
- Explorations, including Escher: [http://euler.slu.edu/escher/index.php/Hyperbolic_Geometry]
- Wikipedia, of course: [http://en.wikipedia.org/wiki/Uniform_tilings_in_hyperbolic_plane]
- Felix Klein: [http://math.ucr.edu/home/baez/klein.html] (Scroll down for a tiling by congruent heptagons)
- Coxeter and Escher (follow links from here): [http://www.ams.org/samplings/feature-column/fcarc-circle-limit]

- Crochet [http://www.theiff.org/oexhibits/05b.html]

- We went over the HW2 questions
- Tilling in Euclidean Plane (Triangles, Quadrilateral Hexagon)
- Tilling in Poincare's model
- Tried tiling with 5 and 7 triangles around one vertex, ended up with hyperbolic paper, talked little about curvature

-Mingzhi Liu