The Double Bubble Theorem

How does soap make bubbles? Why are bubbles round? What shape do two bubbles make when they connect? Although these might seem like questions with obvious answers, the science and math of soap bubbles has all kinds of unsolved problems. In this video, we'll learn about surface tension and the chemistry and physics of soap, we'll learn a fun proof that bubbles should be round using a technique called Steiner Symmetrization, and we'll learn Plateau's Laws for determining the shape of a bubble cluster.

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0:00 Introduction
1:28 Surface Tension
3:47 Surfactants and Soap
4:53 Why are bubbles round?
7:40 Plateau's Laws
10:38 Conclusion

Thank you to Caleb Birtwistle for captioning!

Best overview: Frank Morgan, Geometric Measure Theory: A beginner's guide.
Bubble Chain World Record: https://www.guinnessworldrecords.com/...,    • Longest bubble chain - Guinness World...  
Surface Tension: https://michaelberryphysics.files.wor...
More Surface Tension: https://arxiv.org/abs/1211.3854
Steiner Symmetrization: https://math.williams.edu/symmetrizat...
More Steiner Symmetrization: http://www.math.utah.edu/~treiberg//S...
Plateau's Laws proof: https://www.jstor.org/stable/1970949
2D double bubble proof: https://projecteuclid.org/journals/pa...
3D double bubble proof: https://math.berkeley.edu/~hutching/p...
Honeycomb proof: https://arxiv.org/abs/math/9906042
Triple bubble proof: https://arxiv.org/abs/2205.09102
More Geometric Measure Theory: https://maths.anu.edu.au/files/CMAPro...