Reading: EG, Chapter 14 (learn the definition of inversion and also "the facts" at least), Chapter 15. Learn the definition of the Poincare Upper Half Plane model. We will fill in details in class.

Do some research and write a page on the history and significance of non-Euclidean geometry. Name several mathematicians associated with this geometry and tell a bit of what they did and when they did it. Don't focus on the geometric content for this assignment. We will be working on that separately.

Extra: Email in one or two really interesting addresses on the web with information on the history and nature of non-Euclidean geometry.

In order to draw beautiful figures with circles, you will need to know how to circumscribe a circle around a triangle. Draw a "random" triangle ABC and construct with a compass the circle through A, B, and C. See the xeroxed handout.

Given a circle, draw a point P inside the circle and construct the inversion P' of P in the circle (by any one of several methods). Let Q be another point in the circle. Construct the circle through P, P', Q. This will be an example of how we draw a line in the disk model of non-Euclidean geometry.

Imagine a cube sitting inscribed in a sphere. Two faces of the cube are parallel to the plane of a stereographic projection. The vertices of the cube are connected by arcs of great circles to form a "spherical cube", or tessellation of the sphere by quadrilaterals.

The task: Draw (construct) as precisely as possible the image of "spherical cube" by stereographic projection.

This problem has many methods of solution, from purely drawing ones with cross-sections, to methods that use a lot of algebra. You can make 3D models, 2D cross-sections, use coordinates and algebra. You can take your choice. But make a really neat and accurate drawing.