You may think you know how to make a mean pizza pie. You stretch out the dough and eyeball the toppings, but you're still operating in the realm of guesswork. To turn out a truly fine pizza, you need cold, hard math to back you up. You need Eugenia Cheng, a mathematician with the University of Sheffield in the UK.
Cheng turned her considerable skills toward the noble pursuit of figuring out a formula for creating the perfect pizza. She shares her results in a paper titled "On the perfect size for a pizza (PDF)." Go check it out for all the juicy mathematical details.
The paper's abstract is short and sweet: "We investigate the mathematical relationship between the size of a pizza and its ratio of topping to base in a median bite. We show that for a given recipe, it is not only the overall thickness of the pizza that is is affected by its size, but also this topping-to-base ratio."
Cheng's work assumes that the same amount of dough and toppings go into each size of pie. Her formula uses "t" to designate the constant volume of toppings, "d" to designate the constant volume of dough, and "r" for radius. The formula allows for a comparison of the amount of toppings in an average bite across different sizes of pizza. For example, the average bite from an 11-inch pizza will have 10 percent more toppings than the average bite from a 14-inch pizza.
She told Co. Design that smaller pies tend to have thicker crusts, wider rims, and outer edges with a scarcity of toppings. Rolling the dough out into a larger pizza reduces that crust overload, gives a crispier base for the toppings, and aids in a more even distribution of toppings.
Cheng's formula is all about finding balance between crust and toppings, though much of it still comes down to personal preference. You might opt for a smaller pizza to achieve more toppings per bite, or a larger pizza for less chance of a soggy bottom.
The work was funded by PizzaExpress, a UK-based chain of pizza restaurants that was trying to understand sales patterns for different size pies, particularly the popularity of its 14-inch pizza over the regular 11-inch pizza. It seems customers are going for the thinner crust option without thinking too hard about the math behind it.