# 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

- 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): $3$