The Gömböc at UW

Dr. Tamás Novák, Science and Technology attaché for Hungary, recently visited the University of Wyoming campus to deliver a unique and cutting-edge mathematical object. Hungary is known for its mathematical prowess. One well known example of this is the Rubik’s cube, invented by Ernő Rubik. Hungary is back again on the mathematical object scene again with the gömböc, invented by Dr. Gábor Domokos and Dr. Péter Várkonyi.

What is a gömböc? Most people, including many math students, haven’t heard of it, but it is one of the most impressive recent accomplishments in mathematics. A gömböc is like a Weeble, an object with only two equilibrium points—one stable and one stable. Push it in any direction, with any amount of force, and it will end up settling in the same position. Unlike a Weeble, however, the gömböc is not weighted but homogeneous throughout. Thus, its ability to self-right is due to the shape itself. This makes it the first known object of its kind. You can learn more about the gömböc and its applications on its website.

UW now has two, thanks to Cedar Wiseman, Dr. Domokos, and Dr. Novák. Wiseman is a lecturer in Mathematics here at UW, joining the faculty in 2022 after getting his BS and MS here. He has a particular interest in math education, and through that a penchant for obtaining mathematical objects. Wiseman had learned about the gömböc from his high school math teacher and had been amazed by the idea of it, so he ordered one.

To his surprise, shortly after it arrived he received an email from Dr. Domokos and an offer for an additional custom gömböc, dedicated to UW. Dr. Novák delivered the custom gömböc personally. Wiseman and Dr. Jason Williford, Department Head of Mathematics and Statistics, helped organize his visit with assistance from the Global Engagement Office.

The unveiling occurred in a small ceremony attended by President Ed Seidel, Wiseman, Dr. Williford, and a contingent of faculty from the Mathematics and Statistics Department. In addition to the ceremony, Dr. Novák discussed the possibility of further academic partnerships with Dr. Williford, President Seidel, and Dr. Caroline McCracken-Flesher.

The applications for the gömböc range from engineering and physics to biotechnology and art. It is also a useful educational tool for students in, a capacity Wiseman is excited to try in class. “The basic concepts surrounding it are things that show up in any undergraduate mathematics curriculum,” said Wiseman. “For example, the concept of an isomorphism is something that every undergraduate mathematics student is going to encounter in some capacity, which the gömböc can be used to talk about.” There are further educational purposes from it as well, in undergraduate and graduate mathematics focused on geometry, topology, and more.

Dr. Novák discussed these with President Seidel and the attending faculty, while they unveiled the custom gömböc. To commemorate the dedication to UW, it is engraved with an 1886. More than anything, though, everyone just wanted to test it out.

The gömböc is available to view in the Math Department’s display case in the Center for Assistance with Statistics and Mathematics.