Each project involves exploring a topic covered in class in more depth. There will be two projects, each worth 10% of your semester grade.
Project 1 (due October 25th)
Projects should be about 5 pages typewritten (double-spaced) including diagrams. You may do the projects in pairs. Each person will receive the same grade. Here are some suggested topics. You may choose a different topic related to the course, but it must be approved by me.
A Day in the Life. Create a fictional character who lives in one of the cultures we've read about and who does math. For instance, your character might be an Egyptian tax-collector, or an Nigerian woman who sells goods at a market. Write the story of a day in which the character makes some mathematical calculations, and give details of how the calculations are done. You'll need to do some research to provide accurate details about the character's life.
Fantasy Math. Create your own number system, as J.R.R. Tolkein did in the Lord of the Rings. You'll need both spoken names and symbols for your numbers, and a finger counting system if you wish. Include a multiplication table for the numbers 1 through b+2, where b is the base of your system. Write a "history" for your number system, including a description of the (fictional) culture that produced it and the reason why the base was chosen. The only restriction is that your system can't be base 10, 2, 5, 12, or 60 (since we've already studied examples like this).
Napier's Bones and Genaille-Lucas Rulers. Napier's Bones, invented in 1617 by John Napier, were one of the first pocket computation aids to be popular. Explain the history of Napier's Bones and how they relate to geloisa multiplication. Genaille-Lucas rulers were an improvement on Napier's Bones invented in the late 1800's. Make your own set of Napier's Bones and explain how and why they work. Print out a set of Genaille-Lucas rulers and explain how to use them.
Mathemagic. Report on the use of alphabetic numerals to
create ``magic'' correspondences between words, or between words and numbers.
This is called gematria in the Jewish tradition, isopsephy
Greek, and ksisab al jumal in Arabic. Use this method to make
some predictions of your own.
Project 2 (due December 10th)
Projects should be attractively presented on a standard-sized poster. An essential component of the project is a 5-minute presentation of your poster to the class. You may do the projects in pairs. Each person will receive the same grade. Here are some suggested topics. You may choose a different topic related to the course, but it must be approved by me.
Sona for the 21st century. Create sona drawings relevant to your own life, using traditional sona construction methods. Use them to tell a story, or discuss the mathematics you needed to draw the sona.
The chased-chicken sona. Analyze the chased-chicken design in the same way we analyzed the plaited-mat design in class. What are the possible number of rows and columns of dots? How can you predict the number of lines needed to make the design?
African wallpaper patterns. Just as there are 7 different strip patterns, there are 17 different types of wallpaper patterns--repeated patterns that cover an entire plane. Using motifs from African art, create an example of each of the 17 patterns.
Estimating Pi. There are a multitude of ways to estimate
the number Pi (the ratio of the circumference of a circle to its diameter).
Use at least 3 different geometric methods to estimate Pi and demonstrate
your experiments on a poster.