Need a new party trick? Mathematicians from the University of Liverpool have developed fancy geometric designs that can be used to cut a pizza into equally sized slices.

Joel Haddley and Stephen Worsley expanded on a previous design that shows it is possible to cut a pizza into 12 identical pieces by first cutting six curved pieces, and then slicing those in half. In mathematics, this process is known as monohedral disc tiling, and there is actually a precedent of using pizza slices to discuss the geometry of circles. The researchers from the University of Liverpool write, "Such tilings are produced on a daily basis by pizza chefs by taking radial cuts distributed evenly around the centre of the pizza."

University of Liverpool

By changing the original curved slices into shapes with an odd number of straight sides, you can make more complex patterns with equally sized pieces. The shapes of the slices are referred to by the number of straight sides they have: "5-gons," "7-gons," "9-gons," etc. Like the curved slices, the 5- or 7- or 9-gons are cut in half to create the patterns shown below.

University of Liverpool

A circle can be infinitely divided up this way into smaller and smaller segments. You can read all of the details in a paper published by arXiv, titled "Inﬁnite families of monohedral disk tilings." Haddley and Worsley even took their pattern a step further and demonstrated that you can cut notches of various sizes into the slices to really challenge your pizza-slicing skills.

University of Liverpool

"I've no idea whether there are any applications at all to our work outside of pizza-cutting," Haddley told New Scientist. He has tried to cut a pizza using 3-gons, and simply says that the results are "interesting mathematically, and you can produce some nice pictures."

Source: New Scientist

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