BYU

Abstract by Darian Comsa

Personal Infomation


Presenter's Name

Darian Comsa

Co-Presenters

None

Degree Level

Undergraduate

Co-Authors

None

Abstract Infomation


Department

Mathematics

Faculty Advisor

Gary Lawlor

Title

Arbitrary Volume Triple Bubble

Abstract

3M

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.