Minimal network between three points

Choose three cities in the map by moving the points \(A, B, C\) to the desired location.

(In order to work, the points \(A,B,C\) should be chosen clockwise.)

The minimal (shortest) network of roads that links those three cities is displayed automatically.

(The following applet was produced with the help of JavaSketchpad)

In order to understand why this is the configuration of the shortest network for the three cities, you may consult Fermat's problem and the construction obtained by Torricelli's method or by Simpson's method.