Exam 2 Informal Geometry
Wallpaper patterns (including trip to cathedral), spherical geometry.

Expect some or all of the following questions:
1. Compare and contrast Euclidean, and spherical geometry. What can you say about the following topics in each of the geometries: geodesics, polygons (which ones exist, which ones don’t), sum of the angles in a triangle, regular and semi-regular tessellations (how many?), isometries, area, Escher’s use of each.
2. Explain everything you know about spherical geometry. (Discuss: geodesics, polygons, sum of the angles in a triangle, regular and semi-regular tessellations (how many?), isometries, area, Escher’s art based on spherical geometry)
3. Symmetry Groups. What is a symmetry group? List the elements in a symmetry group. List some subgroups. Note that we have discussed the symmetry groups of polygons (rosette symmetry groups) and the symmetry groups of borderpatterns. Know how to “multiply” isometries. (For example M1xM2 etc.)


Expect to be asked to do the following:
1. Compute the area of a triangle on the sphere. (I will give you the formula)
2. Find a wallpaper pattern for a given tessellation.


The test covers Homework 5,6 (The Cathedral trip), and 7 and any exercises we have done in class.