Date of Award
Master of Science (MS)
A theorem commonly known as the Discrete Pancake Theorem states that for two finite disjoint sets S and T of points in a plane where the union of S and T contains no three collinear points, there exists a line that simultaneously bisects |S| and |T| within an error of at most one. This thesis considers a more general situation in which each point is assigned two non-negative weights and, instead of simply bisecting the plane to obtain a balance in the number of points, we prove there exists a line that simultaneously balances weight one and weight two accumulations within a prescribed tolerance. The Discrete Pancake Theorem is shown to be a special case of this Dual-Balanced Theorem, and a computational implementation of this generalization is applied to various examples.
Denault, Jacob, "A Generalized Approach To Partitioning Weighted Points In A Plane" (2023). Theses and Dissertations. 5241.