Geometry of Pringles: The Crunchy Hyperbolic Paraboloid

The iconic Pringles' hyperbolic paraboloid shape is more than just a geometrical statement, it's a widely exploited structural design.

"You don't just eat 'em", that's the catchphrase of the popular American chip brand Pringles.

And, indeed, if you're an engineer you would do (or think) much more than just eat Pringles.

Your technical curiosity would be tickled by the fact that each Pringle is designed to take the geometry of a hyperbolic paraboloid.

You're also probably wondering now how the bottom-most Pringle doesn't crack with all of the other Pringles stacked on top of it. Apart from the fact that a Pringle naturally fit between your tongue and the roof of your mouth, why is the chip's hyperbolic paraboloid geometry so special?

And how is this particular geometry exploited in architecture and engineering?

Allow us to explain why this unique geometry is fascinating.

What is so special about a Pringle's hyperbolic paraboloid geometry?

Perfectly executed geometries are always pleasant to look at as their natural proportions are simply eye-catching. Just like how a perfectly symmetrical human face, that is naturally proportioned with the golden ratio, is always deemed beautiful or pretty. In the case of a Pringle chip, its intersecting curves form a sturdy structure as well as an attractive geometry.

This special geometry is referred to as the hyperbolic paraboloid in the world of mathematics.

What is interesting about a hyperbolic paraboloid is the point where the maximum and the minimum of the two principal curvatures meet each other at a zero point. This is known as the saddle point or the minimax point.

So, what makes it particularly interesting?

The hyperbolic paraboloid's intersecting double curvature prevents a line of stress from forming, which doesn't encourage a crack to naturally propagate. That's why Pringles have that extra crunch in them when you either bite a piece off or when you put a whole Pringle in your mouth.

If you frequently eat Pringles you would know that they never break off symmetrically but instead, they crack in different directions and produce flakes with varying shapes. It's all due to the hyperbolic paraboloid geometry of each chip.

The intersecting point of the hyperbolic paraboloid is known as the saddle point

[Image Source: Eric Gaba/WikimediaCommons]

Moreover, the two opposing curves perform well together under tension and compression, which give each Pringle some structural strength despite their relatively thin shape.

The geometrical sturdiness of a hyperbolic paraboloid is widely exploited in architecture and engineering especially in structural roof construction. The London Velodrome, the Scotiabank Saddledome in Canada, and the Scandinavium in Sweden are some of the more sophisticated structural examples of a hyperbolic paraboloid in action. 

London Velodrome's hyperbolic paraboloid roof
The London Velodrome, Source: Hopkins Architects

The practicality of hyperbolic paraboloid chips

It's obvious to anyone that the shape of Pringles makes stacking the chips advantageously easy. Again, this is due to their saddle surface that allows the chips to be smoothly placed on top of each other. And as for the Pringle that is placed at the very bottom of the tube, it's able to retain its shape without breaking because the net weight of the chips doesn't usually exceed 150 grams. Plus the hard body of the tube, made possible because of the hyperbolic paraboloid geometry, minimizes the chance of breaking the chips when they are being transported.

From potato chips to structural roofs, this unique geometrical wonder is truly fascinating.

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