Some Comments on the IA/IB Geometry Course

It is not my usual practice to provide printed notes for lecture courses. (You can find printed notes for the course as it was given in 1998 by clicking here .) However, as an experiment, I supplemented my lectures for the Geometry course (given in Summer 2000) with a few web pages. The idea was that these should contain thoughts that I might have expressed in lectures, but which were not appropriate for lecture notes themselves. They were intended to make it easier to understand the notes and see what the point was of the various theorems that were proved. The course is now over, but I hope that these pages may still be found useful.

This page is a handout which I produced for the final lecture, which according to the schedules was supposed to contain an informal discussion of curvature. It is in a dvi version. If you prefer a ps version then click here instead.

Otherwise, I have written on the following questions.

What makes this course interesting?

What makes it hard?

What makes hyperbolic geometry particularly hard?

What can I do to make it seem less hard?

How can the arc of a circle be considered straight?

Why did people want to prove the parallel postulate?

What is the historical importance of non-Euclidean geometry?

What is geometry?

Why isn't it just obvious that a regular dodecahedron exists?

Many pretty pictures, aids to visualization and further explanations of hyperbolic geometry can be found at this site . (I found it by a Google search. It was just the tip of an iceberg.)