Abstract by Darian Comsa
Arbitrary Volume Triple Bubble
Minimizing the surface area of three-dimensional volumes has not been completely proven for more than two arbitrary volumes. The mathematics behind the simple sphere get complicated and lead to bigger questions involving higher-dimensional volumes and perimeters. The natural world often deals with more than just one volume and the solution to minimizing surface area varies with the number of volumes needed to be enclosed. The problem to date is to find the unique shape and prove the minimum surface area for enclosing three arbitrary volumes. The use of interval calculus and two-dimensional slices provides the flexibility of computation for the volumes to be different from each other and thus, changes in surface shape can be accurately measured against the ideal triple bubble. My work has been focused on learning the concepts of the proof and the nuances of Mathematica coding while the paper is being prepared for peer review and future work may be directed on the quadruple bubble in the plane.