# Three Coalescing Soap Bubbles

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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.

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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

"Three Coalescing Soap Bubbles"

http://demonstrations.wolfram.com/ThreeCoalescingSoapBubbles/

Wolfram Demonstrations Project

Published: September 24 2013