2001 GER Minimal distance
Source: 41. Mathematik-Olympiade, Bundesrunde, Klasse 13
June 26, 2019
geometrycombinatorics3D geometrysphere
Problem Statement
Minimal distance of a finite set of different points in space is length of the shortest segment, whose both ends belong to this set and segment has length greater than .
a) Prove there exist set of points on sphere with radius , whose minimal distance is greater than .
b) Does there exist set of points on sphere with radius , whose minimal distance is greater than ?