Pizza Math Yields New Formula for Infinite Curved Slices


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The title “mathematician” may not scream life of the party, but Joel Hadley and Stephen Worsley of the University of Liverpool have shown that they’re at least interested in sharing a meal with each other.

And if the math holds, they’ll be able to split a pizza with as many people as they want ad infinitum! No word yet on whether there are any takers, but the math seems pretty compelling.

Building off the discovery of the monohedral disc tiling pizza (what? you don’t cut your pizza like this now?) that cuts 12 identical slices — six without crust and six with — in a curvy and delicious formula shown below, the two pizza geeks set out to figure out whether it was possible to generalize the rule to allow for more curvy goodness in equal proportions.

Joel Haddley

The image above shows how to double a pie of three-sided curved slices by slicing from the midpoint of one to the end of another.

Haddley and Worsley found that they could cut an infinite number of curved slices with an odd number of sides and even keep the delicate balance when they sliced them each in two. The 5-gon, 7-gon, and 9-gon — as the different shapes are known — are illustrated below.

Joel Haddley

Fancy mathematical diagrams aside, we all know there’s only one way to test a theorem like this: Lunch.