An introduction to the Double Bubble Conjecture, Plateau's Laws, dihedral angles, 2D and 3D curvature, and the Young-Laplace Equation. Submission to the 3Blue1Brown Summer of Math Exposition 2021 (#SoME1). Timestamps: 0:00 Video Introduction 0:29 Double Bubble Conjecture and Plateau's Laws Introduction 0:58 Dihedral Angles 1:52 2D Curvature 3:58 3D Curvature, Principal Curvatures, and Mean Curvature 5:42 Young-Laplace Equation (minimal surfaces with fixed volumes) 6:39 Review 6:59 Conclusion If you find an inaccuracy in the video, please let me know so I can learn! :) Script, animations (Procreate, Keynote), and music (MuseScore playback) created by me. Sources: Double Bubble Conjecture (scroll down to the section on Soap Films) Proof of the Double Bubble Conjecture ~hutching/pub/db2ann/ Curvature Plateau's Laws for Soap Films %27s_laws Young-Laplace Equation