On Saturday September 23, 2012, Travis Mandel led a discussion entitled "Compass and Straightedge Constructions". Travis discussed some geometry problems that ancient Greek mathematicians attempted to solve using only a compass and straightedge, and we used these tools to bisect an angle, create perpendicular and parallel lines, and prove theorems about constructable numbers. Also, we learned why it is impossible to double a cube, square a circle, or trisect certain angles.
We have the handouts from Travis's talk. You're encouraged to explore the problems on your own.
Straightedge and Compass Constructions
Here are some pictures from the talk. Right click and select 'view image' to see it larger.