Shortest Networks Connecting Three and Four Nodes

Determine the positions for the "Junction Points" that minimizes the total length of the edges needed to connect the THREE nodes

in a network. Most often you need to add a junciton point and that piont needs to be a "Steiner Point" to minimize the distance.

Can you move the three nodes around so the optimal solution does not include a junction point? How does that happen?

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Determine the positions for the "Junction Points" that minimizes the total length of the edges needed to connect the FOUR nodes in a network.

This gets more complicated, where you usually need two internal junction points.

However, what do you notice about the angles surrounding the junciton points in an optimal shortest network. They must also be Steiner Pionts.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

John Maharry, Created with GeoGebra