Minimal Connector

This problem is suitable for both KS4 and KS5 students. It is based on a problem from the book Teaching Mathematics as if the Planet Matters

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.

Here is a video showing how a soap film can be used to find the minimal connector.

Here are some resources from the Royal Institution on the same problem.

This video from Matt Parker investigate minimal surfaces and has some nice bubble demonstrations in it!

This paper from Dr. Cyril Isenberg (MBE) explains how soap film can be used to solve problems.  In this video Dr. Isenberg demonstrates some of the properties of bubbles.

This problem is one of a collection designed to develop students' carbon numeracy; we hope it will encourage students to think about the issues surrounding climate change.  You can find the complete collection here.

This problem also featured in an NRICH Secondary webinar in November 2021.