Trisecting the Angle/Hyperbola

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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.


Construction


Proof


Also see


Historical Note

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


Sources