MathDB

Miklos Schweitzer 1978_8

Source: n points in the unit square

January 25, 2009

inequalitiesadvanced fieldsadvanced fields unsolved

Problem Statement

Let

X_1, \ldots ,X_n

n

points in the unit square (

n>1

). Let

r_i

be the distance of

X_i

from the nearest point (other than

X_i

). Prove that the inequality r_1^2\plus{} \ldots \plus{}r_n^2 \leq 4. L. Fejes-Toth, E. Szemeredi