- 1. What are three different types of lines are straight with respect to the surface of a cylinder? Illustrate all three and for each different type of geodesic, give a reason (e.g., a test that relates to reflection in the line symmetry) that explains why it is a geodesic.
- 2. How many geodesic segments (straight line segments) join two points on the surface of a cylinder? Explain and provide illustrations. Structure your response in terms of two different cases.
- 3. Read the paper entitled, “Defining Supports Geometry.” Write a one page, single spaced (with 1 inch margins everywhere) reflection on the paper. Include in your reflection things you found most interesting, surprising, new, confusing, etc. All conscientious responses will receive full credit.
Case 1: the two points lie on the same great circle
Case 2: the two points do not lie on the same great circle
4. On the surface of a sphere, are two triangles congruent if two sides and the included angle of one are congruent to two sides and the included angle of the other (typically referred to as SAS)? If yes, give a convincing argument that tells why SAS is true. If not, provide two counterexamples and explain why each are counterexamples
0 comments