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.

Construction

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Proof

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Also see

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

Historical Note

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

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $3$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3$