Minimal Connector

You can find a network less than 30km long by using two straight lines.

The various approaches use these mathematical skills:

• Alf's method uses spreadsheets and a trial and improvement method, using Pythagoras to find the length of the slanting sides.
• Charlie's method uses right-angled trigonometry and angles of polygons.
• Claire's method uses differentiation (including the chain rule) to find the minimum value.