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 re(2): part 1 spoiler by Charlie)

I see it now.  The problem is equivalent to finding the largest equilateral triangle that can be inscribed with a circle.  The circle, in this case is the cross-section through the sphere created by a plane slicing the sphere, passing through the diameter.

Pythagorus and Euclid both agree with you, and now, so do I.

Posted by MindRod on 2005-12-06 22:46:41