2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58897The classical isoperimetric inequality in R^3 states that the surface of smallest area enclosing a given volume is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of 120 degrees.57 pages, 32 figures. Includes the complete code for a C++ program as described in the article. You can obtain this code by viewing the source of this articleDifferential GeometryOptimization and Control53A10; 49Q05text