# How To Cut Pizza, According To Mathematics

Delicious math. Lukas Gojda/Shutterstock

Over the years, mathematicians have made some pretty important contributions to our lives, ranging from Pythagoras’s geometric calculations to John Nash’s game theory. Now, scientists have finally turned their attention to one of life’s truly big questions: What’s the best way to cut a pizza?

This is not, in fact, the first time that the issue has been broached, with L.J. Upton having first developed a so-called Pizza Theorem back in the 1960s. As the name suggests, the model he developed provided a means of dividing a pizza-shape (otherwise known as a circle) into equal segments.

However, a group of Italian cuisine-loving mathematicians at Liverpool University have now taken this a step further, by calculating ever more complex and eye-catching ways to cut a pizza while still ensuring that each slice remains equal in area. To put that into math talk, they devised a system to create monohedral tilings on a planar disk.

Tiles are said to be monohedral if each one is equal to all others in terms of overall surface area. Previous studies had indicated how this could be achieved by cutting a pizza into six equal "shields," radiating outwards from a central point. These shields could then be divided in two in order to produce 12 monohedral tiles.

Mathematicians had previously shown how a pizza can be split into six or 12 equal "shields." Joel Haddley/Stephen Worsley

However, since these shields aren’t particularly snazzy, the researchers decided to design a more artistic-looking slice, coming up with the following shape. Although all slices are equal in size, the model does not account for the distribution of toppings across the pizza.

Now that's how you cut a pizza! Mathematicians had previously shown how a pizza can be split into six or 12 equal "shields." Joel Haddley/Stephen Worsley

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