Trisecting the Angle/Hyperbola

Theorem

Let $\alpha$ be an angle which is to be trisected.

This can be achieved by means of a hyperbola.

However, the points on the hyperbola that are required for this construction cannot be found by using only a straightedge and compass.

Historical Note

Use of a hyperbola to trisect an angle was devised by Pappus of Alexandria.