MATH3050.06 First Week

First Class

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 11

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 the history of the subject, about applications, etc.)?
* Remember, such questions are required in every assignment!

Second Class:

We will begin with Section 1 of the text: Experiencing Geometry on Pland and Sphere, by David Henderson. This will include a number of small group explorations on 'What is a straight line?' I will provide some 'cones' and 'ribbons' to use in these explorations.

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.
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 Assignment 2. Due September 20 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);
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 . 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.

Third Class:

By the Friday class, we will also consider Section 2 in this text: 'What is straight on the sphere?' While spherical geometry is interesting in itself, one of our basic goals is to understand plane geometry more clearly throught the similarities and differences with spherical geometry. I will bring some plastic 'spheres and rulers' to class, for this exploration. Since we will be exploring spherical geometry for several months, I encourage you to develope your own 'models' for further explorations outside of class.
Second Week of Classes
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