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 examples at the right are networks for four coplanar points at the vertices of a square. None of these patterns would produce a minimal network.
What would be a minimal network for four coplanar points located at the vertices of a square?
A Simpler Problem -- a network for three points
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.
Conjectures - - you construct. Keep a list.
Soap Bubbles - - Try to figure . . .