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.

Also see

 * Trisection of Angle by Parabola
 * Trisection of Angle by Neusis Construction
 * Trisection of Angle by Archimedean Spiral