Soap Films

Minimal surfaces and 120°

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Soap films minimise area: free bubbles are spheres.
• Films meet three at a time at 120° (Plateau’s laws).
• Soap films solve shortest-network problems like the Steiner tree.

Steps

1. Nature minimises
2. Connecting four towns
3. Three towns
4. Two bubbles stuck together
5. Join three towns
6. Why 120°?