Bubble

A bubble is a Minimal Surface of the type that is formed by soap film. The simplest bubble is a single Sphere. More complicated forms occur when multiple bubbles are joined together. Two outstanding problems involving bubbles are to find the arrangements with the smallest Perimeter (planar problem) or Surface Area (Area problem) which enclose and separate $n$ given unit areas or volumes in the plane or in space. For $n=2$, the problems are called the Double Bubble Conjecture and the solution to both problems is known to be the Double Bubble.

See also Double Bubble, Minimal Surface, Plateau's Laws, Plateau's Problem

References

Morgan, F. ``Mathematicians, Including Undergraduates, Look at Soap Bubbles.'' Amer. Math. Monthly 101, 343-351, 1994.

Pappas, T. ``Mathematics & Soap Bubbles.'' The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 219, 1989.