History of Math Ingenuity Professor Simonson

MA 149 Spring 1998

The purpose of these projects is to see how well you have learned to read, understand and communicate mathematical ideas. Your group should meet with me and help define a topic which you will research historically and technically. You are required to write a 10 page paper which consists of an historical introduction to the topic, followed by a survey of particularly interesting results and some of their proofs. You need not prove anything on your own, as you do on the homework, but you must take what you do find and write it in your own words. You should imagine that your audience is one of your peers who knows nothing but high school mathematics. Finally, your paper should conclude with a discussion of your experience while doing the research; including what you found easy or hard to understand and what you found interesting and why. Also, you should discuss any of your own questions or conjectures that arose during your research but were left unresolved.

You are also required to make a half hour presentation of your topic to the class, which should start with a brief introduction in order to provide context. Then you should pick one small result from your paper, and present it in the most interactiive way you can. Your grade will be determined on your communication skills, mathematical content, and how well the lesson works with the class.

Your final grade in the project is 100 ponts for the paper and 50 for the oral presentation.

Some topics in the past:

1. Tanagrams Squaring the Square.

2. Mazes Mathematical Methods of Construction and Solution.

3. Graph Theory Koenigsburg Bridge Problem and Euler Circuits.

4. Tiling Escher Drawings, Penrose Tiles and Periodicity

5. Volumes Methods of Determining Volumes of Various Solids

6. Graph Theory Planar Graphs and Euler's Theorem V-E+F=1.

7. Games: Hex Versus the Shannon Switching Game (Bridgit).

8. GCD Water Jug Puzzles and the Euclidean Algorithm.

9. Probability The Birthday Paradox.

10. Finite Differences Shape Cutting Problems.

11. Regular Polyhedra A Constructive Proof (Euclid) and an Abstract Proof.

12. Coloring What is Two Colorable?

13. Primes Primes of the Form mx+b, Infinite or Finite?

14. Square Roots Methods Throughout History.

15. Irrational Numbers: Geometric and Algebraic Proofs that the Square Root of 3 is Irrational.

16. Recreational Math Polyominoes.

17. Number Theory The Chinese Remainder Theorem.