“Slippery Duck Theorem” Wins National Mathematical Writing Award – Hobart and William Smith Colleges \
The HWS Update

“Slippery Duck Theorem” Wins National Mathematical Writing Award

A paper coauthored by Assistant Professor Jocelyn Bell won the 2021 award for best expository mathematical writing.

“Consider Hathaway’s classical dog-and-duck problem: if a swimming dog heads directly toward a swimming duck, what is the path taken by the dog?”

This is the starting point of “The Slippery Duck Theorem,” a paper coauthored by Assistant Professor of Mathematics Jocelyn Bell and her colleague Frank Wattenberg, a now-retired professor at the U.S. Military Academy at West Point.

The paper earned Bell and Wattenberg the Carl B. Allendoerfer Award from the Mathematical Association of America (MAA), the world’s largest community of mathematicians, students and enthusiasts. Announced in July, the award recognizes the year’s top expository mathematical writing in an MAA publication.

“We really had fun working on this problem, especially investigating limit cycles for different ‘duck paths.’” Bell says.

Bell and Wattenberg’s theorem uses a combination of computer-based exploration and Brouwer’s fixed point theorem to obtain “a general result regarding the long-term behavior of the dog toward the duck.” The topic, they report, lends itself well to undergraduate level student exploration.

“We are absolutely delighted that our slippery duck paper has been selected for a Carl B. Allendoerfer award!” Bell and Wattenberg told the MAA. “We were ourselves surprised by the generality of our main result, the ‘slippery duck theorem.’ As an application of Brouwer’s fixed point theorem, it is a nice reminder that abstract theorems in fields like topology sometimes have practical applications.”

Bell, who joined the HWS faculty in 2016, earned her Ph.D. in mathematics from SUNY Buffalo. Previously, she taught at the U.S. Military Academy at West Point.