Skip to main content
1 of 5
Halbort
  • 1.1k
  • 1
  • 7
  • 20

Optimization of points on a plane

Suppose we have $n$ points on a plane. Let $D$ be the sum of the squares of all the pairwise distances between the points. Let $A$ be the area of the convex hull. What is the minimum possible value of $\frac{D}{A}$ and what arrangement achieves it for specific values of $n$?

Halbort
  • 1.1k
  • 1
  • 7
  • 20