From Euclid to Poncelet: The Rulers of Geometric Constructions

The ancient Greeks were the first to explore ruler and compass constructions, and Euclid was the first to develop a formal theory on them. There are several famous problems that cannot be solved using compass and straightedge, such as trisection of the angle. However, we need not construct with the ruler and compass. We could also use the drafter\u27s dividers, the compass alone, the ruler alone, or even a tool known as the cannon, and using these tools gives us some interesting fields of constructible numbers. In this talk, I will demonstrate the capabilities of geometric constructions and show how they are an exciting way to explore math without using algebra