The mathematics of a pizza bite (by Sheffield University for Pizza Express)

It is now crystal clear.  Eugenia Cheng is both a mathematician and a pizza lover.

A median bite from an 11” pizza has 10% more topping than a median bite from the 14” pizza.

On the perfect size for a pizza

cheng-pizza pdf
Eugenia Cheng
School of Mathematics and Statistics, University of Sheffield
E-mail: e.cheng@sheffield.ac.uk
October 14th, 2013
Abstract
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 affected by its size, but also this topping-to-base ratio.

Acknowledgements: This study was funded by Pizza Express.

The ratio of topping to base in a median bite is given by

where

r = radius of pizza (half the diameter) in inches
d = volume of dough (constant)
t = volume of topping (constant)
α = scaling constant for the edge