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# A Mathematician Finds The Formula For The Perfect Pizza Pie

## Finally, someone does the math on one of the world's most popular, varied—and hotly contested—foods.

There's a formula for pi, so why not for pie (pizza pie)? Pizza—of which the round kind has an area of pi times radius squared—is among the world’s most beloved foods. Yet what constitutes pizza differs greatly and passionately from region to region, city to city, corner to corner.

In Naples, the historic birthplace of the flatbread foodstuff, locals prefer a minimal version cooked quickly in hellish temperatures that yields a soft, springy crust (or cornicione) and a wet center. New York, pizza’s first outpost in the New World, developed a taste for the coal oven, thin-crust kind. (You'd have to stack at least five of these up to equal a deep-dish Chicago rendition.) In Scotland, they still deep-fry it in plenty of chip shops. As pizza picked up in Asia, toppings got adventurous, from calamari and sweet potato to shrimp and, yes, mayo.

Everything about the food, down to its most basic components, seems up for grabs. Even so, one mathematician, Dr. Eugenia Cheng, has developed a formula for the perfect pie, an outstanding claim that could have far-reaching consequences for big pizza business and everyday enthusiasts alike. It all comes down to the crust, she tells Co.Design.

Before we show you the dough, the basics: Based out of the University of Sheffield, the pure mathematician determined a direct correlation between the size of a pie and the experience of eating it. The larger the pizza disk, the rule goes, the more sparingly distributed the toppings are, with fewer bits of pepperoni, sausage, or anchovies (yum) in each bite. A smaller pizza will pack more toppings, and thus, flavor, per mouthful.

"The formula shows just how much more pizza dough is wasted around the edge on a smaller pizza," she tells Co.Design. "The bites in the middle will have too much topping, while the bites around the outside will have too little." How does this distribution of wealth issue effect you exactly? A large, value-size pizza will have a thinner rim of a crust than a medium pizza. The medium's breadier crust, then, encroaches on potential topping real estate. At the same time, the latter will have a thicker base that has a greater chance of turning soggy under the weight of sauce and toppings.

The project was solicited by the U.K. chain PizzaExpress, which, impelled by Cheng’s findings, has added 15 grams of dough to its master recipe. The company had approached Cheng because it wanted to know why its 14-inch pies were selling better than the classic 11-inchers. Cheng's findings backed up consumer preferences for crispier crusts and more balanced toppings.

Pizza is just the latest of Cheng’s food obsessions. Prior to formulating the perfect slice, she had calculated the math behind, among other snacks, Oreos and scones. "I've always used a lot of analogies in teaching, because abstract mathematics is hard to visualize, and analogies from daily life help people see what the point is," she explains about adding some accessibility to research like hers in Higher-Dimensional Category Theory. "Food works a lot like maths actually, because you start with some basic ingredients and then use all sorts of interesting techniques to put it together."

Still, formula and all, Cheng emphasizes that great pizza evades mathematics. Like most foods, it doesn't always seem rational, and variable topping choices can yield unexpected results. "Have you tried potato on your pizza?" she asks. "It sounds like a weird starch on starch combination, but I think it's surprisingly tasty."

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