In this article, we determine and analyse possible solutions to the problem of partitioning a circular cylinder into three regions of equal volume using the least surface area. The solutions are related to the minimal energy arrangement of films in dry aqueous foam confined in a cylinder. We enumerate the possible solutions and use the numerical simulation software Surface Evolver to calculate the area in each case. We determine the least area configuration for all values of the aspect ratio of the cylinder. We find only four possible optimal solutions, each appropriate over different intervals of the aspect ratio, and give closed form expressions for each one.
Keywords
Mathematics, optimization, least area, foam, geometry, Kelvin's problem, Plateau's laws.