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 20080202 04:53:35 