Kara Teehan Develops Mathematical Theorem on Knight’s Tour

Editor’s Note: Distinctive Stockton Students will feature students who receive the Board of Trustees Fellowship for Distinguished Students. This is the third of five posts on the students who received those fellowships this past spring/summer.

Kara Teehan has two more years left before she graduates with a Mathematics degree, but she’s already developed a theorem with her professor—a mathematical feat that many do not accomplish in a lifetime.

Teehan, a native of Middletown in Monmouth County, worked with Dr. Bradley Forrest, an assistant professor of Mathematics, through the Fellowships for Distinguished Students program to explore the knight’s tour problem on cylindrical chessboards. “A knight’s tour is a sequence of moves that a knight can make on a chessboard so that the knight visits each square exactly one time, and a closed tour requires that the knight return to the same square it started from,” Teehan explained.

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To visualize a cylindrical chessboard, imagine a flat board having the flexibility of a sheet of paper in which two opposite edges could easily meet to create a three-dimensional shape.

Although she says she’s not a great chess player, Teehan has found the minimum number of jumps over the cylinder line (where the two edges meet) needed to complete a closed knight’s tour on every sized cylindrical chessboard.

“I found the number of cylinder jumps required for a number of base boards, then formulated an induction argument for larger boards, allowing me to figure out the number of moves on every size board,” she said.

Currently, Teehan and Dr. Forrest are writing a paper for a mathematics journal to reveal their theorem to the world. “I found the material I was studying very interesting and was intrigued by the prospect of being able to create math and discover patterns and concepts no one has yet come across,” she said.

Initially, she was a bit nervous tackling such a momentous puzzle, which is believed to have been first referenced in the 9th century AD and was explored by mathematician Leonhard Euler, who is known for his contributions to calculus and graph theory. However, she quickly discovered her love for pure math, which studies abstract concepts.

“It has been one of the most rewarding experiences; I have discovered I truly enjoy mathematics research, so much so that I want to make a career of it. The fellowship made it possible to engage in this project, and it has opened up doors for me that I did not even know were there, so I am thankful to the committee for selecting me to receive this prestigious honor.”

Teehnan credited Dr. Forrest with tremendous support for her research. “I am very thankful to Dr. Forrest, who is one of the most intelligent, helpful and resourceful people I know, for guiding me through the project and dedicating an enormous amount of time to answering my questions, helping me find resources, being a source of information and editing my work,” she said.

There are still other knight’s tour problems to solve, so Teehan isn’t finished. She will now analyze the same problem on a torus surface. A torus, which is a hollow donut-shape, is made by connecting the two open ends of a cylinder.

As a mathematics tutor at Stockton’s Tutoring Center, Teehan is helping her peers and getting teaching experience for her long-term goal of becoming a math instructor at the college level. “I would like to see math be at the forefront of every student’s education, because I see math in everything and realize how important applications of mathematics are. I hope to encourage other students to become interested in math and mathematics research.”

She’s also a member of Stockton’s chapter of the Alpha Lambda Delta National Honor Society and a member of the math club. She coordinated a division of Cookies4Kids as a part of the Childhood Leukemia Foundation for four years at her local church, and she’s an advocate for Alzheimer’s research and prevention.

Graduate school is Teehan’s next move.