Classic Constructions with a Compass and Straightedge

If someone asked you to draw a regular hexagon, how would you do it? 

Ancient Greek geometers had only a compass (the kind that draws circles, not the kind that you use when you read a map!) and a straightedge (think of a ruler without any markings on it) available to them. Using these simple tools and some geometric knowledge, it is possible to create many accurate angles, shapes and other geometric features. 

Depending on student interest and prior knowledge, students will learn some or all of the following: 
*How to duplicate line segments and angles
*How to bisect (split in half) line segments and angles
*How to create a sets of parallel  and perpendicular lines
*How to construct an equilateral triangle, a rectangle, a rhombus and a regular hexagon. 
*How to construct the center of gravity of any triangle so that it can be balanced on the tip of your pencil

This lesson is useful for students who need more hands-on instruction in their high school geometry course, but the methods learned in this lesson can also be applied to art and design. Armed with these techniques, what will you do next? Build a birdhouse? Create some abstract art?