What is the shape of a Pringles potato chip? According to UA professor and chair of the Department of Mathematics, Dr. David Cruz-Uribe, it looks like a hyperbolic paraboloid. In fact the two look so similar that many math professors refer to the chip when describing a hyperbolic paraboloid to their students, but Cruz-Uribe says no one has gone to the trouble of actually proving it.
Consequently, he turned the question over to his honors calculus III class and asked his students to create a mathematical description and a graphic model of the chip to either prove or disprove the theory.
Cruz-Uribe gave the students six weeks and no help.
“The project required very careful measurement of something that is difficult to measure,” Cruz-Uribe said. “They had to go from the physical object to a mathematical description, and then they had to convert that description into graphical imagery.”
In the end, he was impressed. Nearly a dozen students submitted their work, and four went as far as to create a model of their mathematical descriptions using the University’s 3D printers.
“Pringles were designed so that they would nest perfectly on top of each other in the can,” Cruz-Uribe said while placing one of the 3D models on top of a real Pringles chip. “So, if the models are the real shape, then I should be able to stick an actual chip on top of the model and they will fit perfectly together.”
A few of the models came pretty close. Cruz-Uribe hopes to turn the one-off extra-credit project into a future research opportunity for his students and unveil, once and for all, the shape of the Pringle.