Why A Pringle Is Shaped The Way It Is
From the first time I saw a Pringles tube, I had wondered about why these chips are shaped the way they are, different from the “randomness” of other chips. The simple answer was that Pringles are not made from potato slices, but from extruded potato paste – like the snacks ‘sev’ and ‘chakli’. To be honest, I never thought too much about the shape again till I recently made the connection while revising slope fields and thought about the sketching of quadric surfaces (graphs of polynomials with the highest power of 2 in 3 dimensions). Having now learnt about the maths of this shape, a hyperbolic paraboloid, this story is about the design of the Pringles chip. The shape is called a hyperbolic paraboloid because the equation gives a parabola in two planes (xz and yz planes), and a hyperbola in one (xy plane). One way to think about this is by thinking of cross sections of the curve – like an MRI. If we take a horizontal slices (z = constant) of a Pringle, then we get hyperbolic sections ...