Clairaut's Angle Trisection

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration shows Clairaut's angle trisection, which uses a hyperbola.

Contributed by: Izidor Hafner (September 2012)
Open content licensed under CC BY-NC-SA



Let be the given angle with and on the circle with center . Let the points and trisect the segment and let the bisector of the angle cut at and the circle at . Then . Let the hyperbola with focus , vertex , and directrix cut the circle at point . Let be the orthogonal projection of on and let be the point symmetrical to relative to . Then .


[1] W. W. Rouse Ball, H. S. M. Coxeter, Mathematical Recreations and Essays, 13th ed., New York: Dover Publications, 1987 p. 346.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.