Double Soap Bubble
When a double soap bubble forms, it consists of two spheres that intersect, with a soap film separating the chambers on each side. This separating wall connects with the surface of each sphere at a 120-degree angle. If the two spheres have equal size, then the separating film has the shape of a flat disk. If one sphere is larger, then the separating wall bulges into the larger space enclosed by the larger sphere.
The question of which geometric shape for a co-equal double bubbles maximizes the internal volume baffled mathematicians for decades until it was finally solved in 2002.