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. Become a Patreon member: https://www.patreon.com/PhysicsfortheBirds 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/world-records/longest-bubble-chain-(hanging), https://www.youtube.com/watch?v=TxgxIDJnWzg Surface Tension: https://michaelberryphysics.files.wordpress.com/2013/07/berry018.pdf More Surface Tension: https://arxiv.org/abs/1211.3854 Steiner Symmetrization: https://math.williams.edu/symmetrization/ More Steiner Symmetrization: http://www.math.utah.edu/~treiberg//Steiner/SteinerSlides.pdf Plateau's Laws proof: https://www.jstor.org/stable/1970949 2D double bubble proof: https://projecteuclid.org/journals/pacific-journal-of-mathematics/volume-159/issue-1/The-standard-double-soap-bubble-in-bf-R2-uniquely-minimizes/pjm/1102634378.pdf 3D double bubble proof: https://math.berkeley.edu/~hutching/pub/db2ann/db2ann.pdf 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/CMAProcVol34P2-Morgan.pdf