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(2): Solution by Charlie)

If (like Charlie) I place the following points
in the northern hemisphere

  (0.85953,0,0.51109) and (0,0.85953,0.51109)

and the following point in the southern

  (0.60778,0.60778,-0.51109)

, then I get the following distance between
points

  1.21556

Posted by Bractals on 2008-02-02 04:53:35