We arrive now at our third of three problems of antiquity, the angle trisection problem. Again, we will look at the origin of this problem in history, some ways the ancient Greeks solved it, some modern ways of solving it, and the eventual solution to the problem.
If you are interested in one proof that an arbitrary angle cannot be trisected, you can see Proof of the Impossibility of Trisecting an Angle with Euclidean Tools. The proof we’ll look at in class is essentially that of the third reading.
Readings
First Reading: Trisecting an Angle
Second Reading (Video): Trisecting the Angle and Squaring the Circle
Third Reading: Proof that one can not Trisect an angle of 60 degrees with Straight Edge and Compass
Fourth Reading: How to Trisect an Angle (Not!)
Finally, here’s a nice concise summary of the Three Problems. Three Greek Problems of Antiquity