Mathematicians at the University of Liverpool researching a long-standing mathematical conundrum have found their results can be applied to the art of pizza cutting.
They began by looking at an existing result which showed a way to cut up a circle beyond the obvious way, which was to cut the circle with number of lines from the centre to the edge, as one would if cutting up a pizza.
They then looked to see if there were other ways to cut a flat disc into equal-sized pieces with some pieces not touching the centre and found that this was possible.
Stephen Worsley said: “Our research explored a long standing maths conundrum of cutting a flat disc into equal-sized pieces. We knew solutions existed, however, we were interested in demonstrating a surprising solution where some of the pieces did not touch the centre.”
The researchers demonstrated that it is possible to cut a flat disc into scythe-shaped, curved slices with any odd-number of sides – known as 5-gons, 7-gons, 9-gons.
Dr Haddley, who has actually tried slicing a pizza this way (see above), added: “Mathematically there is no limit whatsoever to this although it might be impractical to carry out the scheme beyond 9-gon pieces.”
“I’ve no idea whether there are any applications at all to our work outside of pizza-cutting but our results are interesting mathematically, and you can produce some nice pictures”.
The research is published in a paper entitled “Infinite Families Of Monohedral Disk Tilings.
An article was published in New Scientist about these research findings and it has been covered widely in the media.
Photo credit – Dr Joel Haddley