Problem:
What is the minimum length of a network spanning four coplanar
points located at the vertices of a square?
A network can be made shorter by adding other points to connect
line segments. The following are networks for four points.
None of these patterns would produce a minimal network. What
would be a minimal network?
1. Four points at the vertices of a quadrilateral other than a square.
2. Four random points.
3. Five points on a convex pentagon.
4. Six points on a regular hexagon.
5. Six points in a 2 by 3 rectangular grid.
6. Nine points in a 3 by 3 rectangular grid.
7. Twelve points in a 3 by 4 rectangular grid.
8. Sixteen points in a 4 by 4 rectangular grid.
9. Twenty-five points in a 5 by 5 rectangular grid.