#### Date of Award

5-2017

#### Degree Name

Bachelor of Science in Mathematics

#### First Advisor

Dr. Zach Teitler

#### Abstract

In a 2006 paper [1], mathematician Thomas Banchoff posed a new calculus problem, when he filled two cups with coffee. One was convex, while the other was concave, but in such a way so as to fit together perfectly. These cups were thus, complementary. The next natural question he asked was "Which cup has more volume?", so that he could be gracious enough to give the larger of the two to his wife. Banchoff decided to explore this topic, but he left some unanswered questions along the way. Under what conditions would two Complementary Coffee Cups have the same volume? Does the answer depend on the curve between the two cups? Can a coffee cup be complementary to itself? If so, under what conditions does this occur? Does the volume of a pair of solids have anything to do with lateral surface area. This paper will explore the mathematical relationship between pairs of complementary coffee cups by answering these questions.

#### Recommended Citation

Sams, Brandon, "Complementary Coffee Cups" (2017). *Mathematics Undergraduate Theses*. 6.

https://scholarworks.boisestate.edu/math_undergraduate_theses/6