Student Talk: Folding a Pringle: The Secrets of the Hyperbolic Paraboloid

Abstract: There are many mathematically-interesting foods, but Pringles are quite the stand-out. Why? They are a model of a shape called a truncated hyperbolic paraboloid, which is like a hybrid of a hyperbola and a parabola, the way that a sphere is like a hybrid of two circles. But a hyperbolic paraboloid is very different from a sphere in many ways. For one thing, it is negatively curved everywhere, whereas the sphere is positively curved everywhere. In this activity, I will show what this means, and how negative curvature can arise from a flat piece of paper. I will do this by showing how to fold an approximation to a truncated hyperbolic paraboloid. I will discuss the interesting properties of this shape as well as the other shapes belonging to this family of surfaces, the quadrics. I will also describe the kinds of shapes that are possible by joining these truncated hyperbolic paraboloids together at their boundaries.

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