MATH3050.06 First Week

Since I will ask you to give your 'geometry autobiography', I have posted by own geometric autobiography for you amusement! I hope it gives you some small insight into my own questions and a slice of my own 'mathematical life'.

Assignment 1. Due September 13

Write a short (roughly 2-5 page) 'geometry autobiography', including items such as:
  1. What has been your previous exposure to formal geometry (as in high school courses, summer jobs, applications to other fields etc.)
  2. What has been your previous exposure to informal geometry: hobbies (origami, sewing, carpentry etc.), sports, observing nature, design?
  3. Why geometry is taught in high school?
  4. * What are a couple of key questions you would like to find answers to during this year of geometry (including possible questions about learning, about 'proving', about visual thinking, about the history of the subject, about applications, etc.)?
* Remember, such questions are required in every assignment! You must include them in this assignment.

Explorations at the First Class

We will begin with Section 1 of the text: Experiencing Geometry on Plane and Sphere, by David Henderson. This will include a number of small group explorations on `What is a straight line?' I will provide some spheres, cones, paper and ribbons to use in these explorations.
We will work on this in the first class. Make some notes to bring to at the second class and I will ask you to discuss your ideas in small groups. After this discussion and whatever questions you have in the second class, I will ask you to begin to write up your response to Problems 1 and 2 in the text. We will have some additional time to discuss your ideas and questions - and the assignment is due September 25.

I will hand out a problem on "bicycle tracks". This is actually directly related to the idea of what it looks like and feels like to turn - and to the idea that straight means not turning.

Here are a couple of web pages related to `straight' and 'curving' paths (courtesy of Eli Brettler):
Some text for the bicycle track exercise.
Some sample tracks to apply the exercise on sample tracks.
Remember, these tracks either fit a bicycle moving forward up the page or down the page (but not both). Which is it? Can you prove your answer is correct?
What is the connection between this exercise and the question `What is a straight line'? You can discuss this within Assignment 2 (below).
I have now posted some hints on analysing the bicycle tracks

Assignment 2. Due September 25

Write your solutions to Problems 1 and 2 in Henderson. In writing this, you should make use of:
  1. what was discussed in class, either as a whole group or as in small groups;
  2. suggestions in the book;
  3. your own experiences and examples (including the bicycle track exercise above);
  4. some connections between straight lines and symmetry.
The written response will be individual, but you are encouraged to discuss your answers with other students inside and outside of class.
* Remember to include your questions on every assignment. These may be directly related related to the assignment; a continuation of a dialog begun in the first assignment; or questions provoked by experiences outside the course. Such questions / dialog are required in the assignment.

Other Students?

The class is not full. If you know other students who are interested in the course, they should get in touch with me immediately.

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