Math 465: Foundations of Geometry

Math 584: Euclidean and Non-Euclidean Geometry

Information Page, Fall 2010

I will be in my office on Friday, 12-1pm. Come by to see your final. Or e-mail me to get your score and final grade.

Nine point circle

Here are some properties of the nine-point circle.

Here is a discussion of the Simson line, and here is a proof of the Simson's line theorem.

Here and here is a discussion of Miquel point.

Here is a nice article about finite geometries.

Here is a short discussion of affine and projective planes.

Here is an overview of Hilbert's axioms.

Here is a nice discussion of inversion. See various links at the bottom which all show various applications of inversions. In particular, read the one about Apollonian circles theorem, which is related to problem 39.10.

Here is another place where many interesting results related to inversion are discussed.

Here is a short discussion of inversion with many references.

Here is a very nice applet showing the Poincare model of the Hyperbolic plane. Play with it!

Here is another nice applet.

Here is a more substantial discussion and visualization of hyperbolic geometry.

You should be able to state and discuss the five postulates from the Elements and the main definitions of Books 1-4. You should be able to state, prove, and use the following propositions from the Elements.

Book 1: Propositions 8, 9, 10, 11, 12, 23, 26, 27, 29, 31, 32, 47.

Book 2: Propositions 11, 12, 13, 14 (squaring a rectangle).

Book 3: Propositions 16, 17, 18, 19, 20, 21, 22, 23, 31, 32, 35, 36, 37.

Book 4: Propositions 4, 5, 10, 11.

Assignments

Assigments must be written carefully. You are allowed (even encouraged) to discuss the assigments with other students but you have to write the solutions on your own. Identical solutions will not be graded. If your solutions are not written clearly, they will not be graded and you will receive no credit.