Cutting a pizza can be a stressful experience: are the slices equal? Now, a team of mathematicians has found some new ways to cut pizzas into exotic slices, while still ensuring that the all-important size considerations are met.

The slicing of pizza is an oddly well-researched area of mathematics, principally because it has less to do with pizza and more to do with circular geometry. But that doesn’t stop the team from Liverpool University focussing on the fact that it’s really investigating a way to slice everyone’s favorite bread-based meal.

The work builds on previous research that showed that it was possible to cut a pizza into six curved slices (or ‘shields’), each of which could then be sliced in half to produce 12 identical slices. Like this:


The new approach shows you can use a way more complex pizza slicing approach that still yields equally sized pieces. It relies on creating initial pieces that resemble the curved shields above, but which this time are instead made up of an odd number of straight sides. Each of those can then be cut up into equal slices. Like this:

You can, according to the researchers, keep going indefinitely, increasing the number of sides of the shield as you go. (Read all the technical details right here if you want.) You can even add in some extra notches to make things look really weird:


But go easy, or you might need a very accurate pizza cutter indeed.

[arXiv via New Scientist]

Top image adapted from Shutterstock. All other images by Joel Haddley/Stephen Worsley.