You can choose to do a small project instead of the second in-class exam. You are free to choose the topic for your project, but you need to get it approved by the instructor. Some suggestions for topics are given below.
The project should include a study of a small part of geometry somehow related to the course. You will need to
* Write a short report, 3 - 5 pages, due Friday November 21st.
* Give a short presentation, 5 - 10 minutes, during class on Friday November 21st.
The instructor can help with some of the books suggested for study below. In addition to the suggested reading, feel free to surf around. Google Scholar can be a great starting point.
Possible questions Describe Moulton's model. Discuss convexity in the model. How many parallels are there in the model? Is Desargue's theorem true for the model?
Suggested reading A Simple Non-Desarguesian Plane Geometry by F. R. Moulton, Transactions of the AMS, Vol. 3, No. 2 (Apr., 1902), pp. 192-195
Possible questions How does congruence work in taxicab geometry? Real-world applications of taxicab geometry?
Suggested reading Taxicab Geometry : an adventure in non-Euclidean geometry by E. F. Krause, Dover Publications, 1987, ISBN 0486252027.
Possible questions History of the problem. Why is it not possible to trisect an angle using a compass and a straightedge (this is typically shown using algebra, so it may be a bit on the side of the course)? It is possible to trisect an angle using a twice marked straightedge and a compass.
Suggested reading Constructions Using a Compass and Twice-Notched Straightedge by A. Baragar, The American Mathematical Monthly, Vol. 109, No. 2 (Feb., 2002), pp. 151-164.
Possible questions What happens if we introduce the horizon (points at infinity) into euclidean geometry. How is perspective related to the horizon? how is perspective used in drawing/art?
Suggested reading Chapter 3 in Yearning for the impossible : the surprising truths of mathematics by J. Stillwell, A K Peters, 2006, ISBN 156881254X.
Possible questions What was the impact of The Elements? How is our treatment of elementary geometry different from Euclid's. What was the role of Pasch, Peano, Hilbert, Birkhoff, etc.? How has geometry developed the last 80 years?
Suggested reading Mathematics and its history by J. Stillwell, Springer, 2002, 2nd. ed., ISBN 0387953361.