Putting the 1992 Putnam Test question A-6 into code.

Problem

If you choose 4 points on a sphere and consider the tetrahedron with these points as it's vertices, what is the probability that the center of that sphere is inside of that tetrahedron? (Each point is independently chosen relative to a uniform distribution on the sphere.)

Bouquets

This project was inspired by the video The hardest question on the hardest test by 3Blue1Brown:

Description

The proof discussed in the video is very elegant, but I wanted to see how it worked in practice.

For the random distribution, I create a starting point P(0 | 0 | 1), then rotate it by a random amount around the x-, y- and z-axis for a uniform distribution.

To test whether a point is inside or outside of the tetrahedron, I convert it's vertices into a barycentric coordinate system. For more information, check out this Wikipedia article.

Examples

You can find more examples in /examples or generate your own by running main.rs.