Ancient Greeks were fascinated with what could be constructed only using a compass and a straightedge without markings. They were able to construct many things like bisecting an angle, but others like doubling the cube baffled them. Legend has it that ancient Athenians were told by the oracle at Delos that a plague would end if they could double the volume of the cube at the altar to Apollo with a compass and a straightedge. The ability to show that this and other problems were or were not possible did not come until 2000 years later with the discovery of algebra in the nineteenth century. We will take a look at what it means to be constructable and how one can put these geometric constructions into a plane. I will then touch on the ability to show if there exist any type of relationship between two constructions.
