There are three points on the surface of a sphere centered at origin. One has an x coordinate of 0, another has a y coordinate of 0, and the last has a z coordinate of 0.

What is the biggest possible equilateral triangle that can be made using these three points as the corners? How many equilateral triangles of this size are possible?

What if instead of a sphere, it is a regular octahedron centered at origin, with each of its vertices on an x, y, or z axis?

(In reply to part 1 spoiler by Charlie)

I'm not convinced that there are 4 triangles of maximum size.

Posted by Tristan on 2005-12-05 20:44:00