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 Summary?
Actually that's 1.2091881 units, as the 1.224 is only at the expense of other distances being 1.200. The 1.2091881 is the maximum minimum, as in the last paragraph:
"The points are at latitudes 32.9729085 north and south (where the squares vertices touch the surface of the globe). The two squares are twisted 45 degrees relative to each other in longitude, and the chord distances are 1.2091881 units (in our case earth radii)."
Posted by Charlie
on 2008-02-03 11:23:01