In this talk we will be looking at the classical "straightedge and compass" constructions. We will say that a number, x, is constructible if we can "build" x from a finite number of straightedge and compass constructions (given some beginning unit length). It is fairly easy to see that if we begin with some given unit length, then we can construct any rational number (we will see why this is true). Additionally, if we can construct a number x, then we can also construct its square root (but not its cube root in general).

We will explain how constructible numbers are formed and explore some of their properties. From this, we will give a concrete construction of a regular pentagon and explain why one cannot "square the cube", trisect a general angle, or construct some regular n-gons.

This talk should be very accessible and hopefully alot of fun. I hope to see you all there!