# Three Coalescing Soap Bubbles

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Using the calculus of variations, the Belgian mathematician Joseph Plateau deduced that the interfaces between adhering soap films represent localized minimal surfaces, which occupy minimum areas around a set of constrained geometric regions. Of course, this is not a global minimum, which would consist of a single spherical bubble. This Demonstration considers the case of three connected bubbles with variable radii, centered at , , and . You can also choose to see the details of Plateau's construction.

[more]
Contributed by: S. M. Blinder (September 2013)

After work by: Enrique Zeleny

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Reference

[1] C. V. Boys, "Soap-Bubbles and the Forces Which Mould Them," London: Society for Promoting Christian Knowledge, 1896. www.gutenberg.org/files/33370/33370-h/33370-h.htm.

## Permanent Citation