How to Mathematically Cut a Pizza to Infinity
Pizzas are simultaneously the best and worst party food. The good? They're delicious. The bad? When you need to feed a large crowd, the only solution is more pizzas (OK, that's not necessarily a bad thing). Don't even start with that grid-cut nonsense. You can't put a square cut on a round pizza. I think that's in the Bible.
Thankfully, we have scientists and mathematicians who are ready to solve the dilemma of pizza politics. Joel Haddley and Stephen Worsley of the University of Liverpool have devised a way to cut pizza that can be parsed ever smaller to create an infinite number of (extremely unsatisfying) servings. Their process is a new take on the monohedral disc tiling method, which creates six curved slices or, when divided in half, 12 equally sized slices that serve the interests of both crust-lovers and crust-haters alike. It looks like this:
Taking this to the next level, Hadley and Worsley propose that by cutting a pizza into polygons with odd numbered of sides (5-gons, 7-gons, 9-gons, etc.) and then dividing those shapes in half, a limitless potential for slices emerges. Cutting wedges into those shapes can also produce some stunning patterns that, while probably impractical, would totally impress your stoner friend who suggested ordering a pie in the first place.
“I’ve no idea whether there are any applications at all to our work outside of pizza-cutting,” Haddley told New Scientist, "[the results are] interesting mathematically, and you can produce some nice pictures.” I've been a poor college student, and I can tell you one thing: splitting a single pizza between an infinite number of people definitely has applications.
[h/t New Scientist]