Eight points are placed on the surface of a sphere with a radius of 1. The shortest distance between any two points is greater than 1.2. How can the points be arranged?

Hint: They are not arranged as a cube. The cube would have an edge length of only 2/sqrt(3) = 1.1547.

(In reply to re(5): More for Charlie's thoughtful consideration by Charlie)

Charlie wrote:
If we move two diagonally opposite (separated by 180-degrees of longitude) points in the southern hemisphere without moving the other two southern points north toward the equator, they will be closer to  those other two southern points, as they are on a lesser circle around the south pole, not the great circle that is the equator. So the separation is less than d0 even within that southern square.

Which is right

 

Posted by FrankM on 2008-02-11 21:36:15