Created by
Created May 2011 by
L. Straube and K. McCarthy
with input from A. Hart and K. Burns
Assignment with Due Dates
Senior Math Survey
Final Project
You will choose a math topic to research, write about and present to your classmates.
There are two parts to this project
- Choose a topic and research it. Below are some suggestions for topics you may wish to research. You are not limited to these topics and may choose another. You will decide how in depth you will go with the project and what your goal is in doing this research. You may just be presenting information or demonstrating the topic to your classmates, or you may actually involve them in hands on activities. Your topic and an outline of your research should be discussed with me and approved before you begin working on your presentation.
- Class presentation. You will give a presentation to the class on what you have learned through your research. You should include some visual aids in the presentation, which may involve demonstrating sample problems or showing diagrams. You should also have the class be actively involved at some point in the presentation. Make sure you understand any material you are presenting. You will be expected to answer questions on the topic.
This Project is worth 50 points.
Timeline:
May 14 – Library
May 15– Library
May 16 - Library
May 17 – Library
Possible topics to choose from (Some of these topics have already been introduced in class. If you choose # 1, 3, 4, 10, 15 or 20 you must go beyond what was covered in class):
1. Investigate the five "perfect" (or Platonic) solids and explain why there are only five.
2. Research an invention based on unusual geometric properties or configurations
3. Learn about the Escher variety of periodic drawings and learn how to analyze an Escher drawing to find the unit cell, etc.
4. Investigate tiling the plane with similar figures (tessellation).
5. Analyze and describe the construction of an accurate sundial (gnomon).
6. Game Theory. Investigate the application of mathematics to game strategies. Zero-sum games, etc.
7. Investigate the technique of linear programming.
8. Research the application of mathematical principles in the world of art with a written description of those principles and their application
9. Investigate ancient number systems.
10. Investigation Beyond the Third Dimension. We perceive our world as one of three dimensions. Mathematicians of vision, however, have ventured beyond these limits, conceptualizing "spaces" of four and even more dimensions. How can we use algebra and geometry to extend our knowledge of the first three dimensions? Can you build a model of a tesseract, the fourth-dimensional equivalent of a cube?
11. Some Special Numbers. The constants 0, 1, i, and e have many important and unique properties. What are these numbers? How are they related to each other? How did they develop in the history of mathematics?
12. Research the role of geometric shapes and properties in architecture and construction.
13. Research a famous mathematician and demonstrate his/her major contributions to the field.
14. Music and Mathematics.
15. Non-Euclidean Geometry. Many attempts have been made to prove Euclid
16. Ciphers, Codes and the way they are broken. Investigate the use of check digits and error detecting codes in use today. UPC bar coding, Social Security numbers, etc
17. How Eratosthenes measured the circumference of the earth.
18. The theory of perspective in drawing
19. Measurement of the distance from the earth to the moon by simple geometry.
20. Investigate the Golden Proportion and the Golden Rectangle in art and nature.
21. The math little kids can do. Investigate how children develop math skills and relate at least three skills to those they will use later in high school math.
Your grade will be determined by me and your peers. You will be graded on preparation (10pts), presentation (10pts) and mathematical content (25pts) and a peer evaluation (5pts).
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