Mathematicians Have Figured Out the Perfect Way to Slice Pizza

Is there a more frustrating sight than a badly cut pizza? The bit with a disproportionate amount of mushrooms, the slice with too much crust, and that single, sad, pepperoni-less slither you just know you’ll end up with after your ‘za-eating companions swoop in for the big pieces.

But uneven pizza slice-induced frustration may soon be a thing of the past. Two mathematicians have come up with a new method of cutting pizza that they say can result in limitless equal slices.

As New Scientist reports, Joel Haddley and Stephen Worsley from the University of Liverpool had already developed a system of dividing up pizza to create 12 identical slices, known as monohedral disc tiling. In their new paper, “Infinite families of monohedral disk tilings” (really gets your mouth watering for all that pizza slicing action) however, the pair prove that there is actually no limit to the number of equal slices a pie can be cut into.

It’s all down to geometry. Generalising their monohedral technique, Haddley and Worsley cut the pizza into curved pieces with odd numbers of sides, known as five-gons, seven-gons etc. These slices can be divided in two an infinite number of times.

Joel Haddley and Stephen Worsley’s diagram for slicing pizza. Figure via “Infinite families of monohedral disk tilings.”

Haddley noted that “there is no limit whatsoever” to the number of pizza slices that can be created using this method. It may be difficult to go beyond a nine-gon piece, however.

The mathematician even went so far as to test out his theory on a real pie, resulting in a star-like design.

Photo courtesy Joel Haddley.

Despite his discovery, Haddley doesn’t seem optimistic about the theory’s uses away from the cheese-layered foodstuff. He said: “I’ve no idea whether there are any applications at all to our work outside of pizza-cutting.”

Eliminating age-old arguments over who got the biggest slice of Meat Feast? Creating a utopia of perfectly equal pizza distribution? You’d be hard pressed to find a better real-life application than that, Joel.