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. To see a proof for just an angle of \(60^{\circ }\), here is a reference.

1 Readings

First Reading: Trisecting an Angle

Second Reading (Video): Trisecting the Angle and Squaring the Circle

Third Reading: How to Trisect an Angle (Not!)

Finally, here’s a nice concise summary of the Three Problems. Three Greek Problems of Antiquity

2 Questions

In what year were both the cube duplication and angle trisection problems solved by Wantzel? \(\answer [given]{1837}\)
Which of the following is not possible with only straightedge and compass?
Trisecting an angle of \(90\degree \). Trisecting any line segment. Trisecting an angle of \(45\degree \). Trisecting an angle of \(60\degree \).
2025-01-06 15:54:07