Three points are located on the surface of the ellipsoid: 2x² + 2y² + z² = 3. One has a x coordinate of 0, another has a y coordinate of 0, and the last has a z coordinate of 0.

What is the largest possible equilateral triangle (in terms of area) that can be made using these three points as the corners? How many distinct equilateral triangles of this size are possible?

(In reply to a candidate by Charlie)

On second thought, such a displacement would also mean that one of the fundamental plane's was left unoccupied. So, that strengthens the idea that the proposed candidate triangle (or set of 16) is the one sought.

Posted by Charlie on 2010-08-18 16:57:48