A compass is more than just a tool for drawing circles. I remember as a student the first time I used one for that purpose, it was so cool. Later in school I learned all the other things a compass can be used for. Who knew something that made circles, when also used with a strait edge, can also be used to make triangles. That just blew my mind.
It is important to know how to use a compass and strait edge to create angles because with just these two tools, you can accurately make any geometric figure. As early as ancient Greece mathematicians were using these tools to solve geometric problems. In these times though, the compasses were collapsable, that is, they would close as soon as they were moved, and would not hold its radius. A Greek mathematician named Euclid formulated three famous geometry problems that for centuries went unsolved. The basis of these problems were to solve them using only a strait edge and compass.
the three problems are:
1.Squaring a circle
2.Doubling a cube
3.Trisecting an angle
It wasn't until a few thousand years later that it was proven these constructions are impossible to make using only a strait edge and compass.
In elementary geometry, we only go so far as to construct angles, triangles and bisectors, with these tools. Yet these same tools have been used for thousands of years to solve (or not solve) much more complex problems.
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