Care to know how mathematicians divide a pizza?
Like me, you may naively think that the ordinary way of dividing a pizza is good enough. You are clearly not sufficiently overthinking about this. Suppose, for example, that you want to divide a large pizza into 12 slices and half the people like the crust and half do not. Everyone can be taken care of by slicing the pizza like this
I took this picture from Matt Parker’s book Things to Do and Make in the Fourth Dimension, which I borrowed from the library. You may or may not find it relevant that, in addition to being a mathematician, Parker is a standup comic.
In doing Web searches about dividing pizza, I came across a result known as, I kid you not, the Pizza Theorem. It addresses another issue. Suppose that two people want to divide the pizza. In order to divide it in the usual way, you need to locate the center of the pizza. To do this accurately, requires use of compass and straightedge, which can get rather messy on the surface of the pizza. It turns out that you can center your cuts using any point in the pizza, as explained in this video
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16 Answers
Whatever method used, it is a function of pizza PI.
That would have been my guess as well. Somehow Pi must be involved :)
However, I do prefer the first solution since I’m not a big crust fan :)
In the Detroit metro area, Jet’s Pizza scientists eliminated the difficulty decades ago with the rectangular pizza.
Damn you Auto correct !
I ran out of edit time.
It’s Kenji from Serious Eats.
That would be J. Kenji Lopez-Alt, an excellent food writer and researcher. He is the main reason I subscribe to that site. He’s like the folks at America’s Test Kitchen taken up a notch.
Don’t bring an autistic child a square pizza. It gets really ugly really quickly.
If you get into “who likes crust, who doesn’t like crust” then there may not be enough of either type (pieces with crust, pieces without) to please everyone’s needs. Just cut it into triangle slices and for those that don’t like crust, they don’t eat the crust.
Blonde walks into a pizza shop and orders a large cheese.
“You want 8 or 12 slices?” asks the person behind the counter.
“Better make is 8”, she replies. “I’m not that hungry.”
apologies to @johnsblond and blondes everywhere.
@jca, 12 pieces for a large pizza should be right. The 6 people who like crust share it equally, giving them twice as much as they would otherwise have gotten. Those who do not like crust don’t get any. I think it is a pretty ingenious scheme. There are also similar ways of cutting a circle into more pieces, obviously not applicable to pizza division.
@LostInParadise The crust/no crust division may be a nice goal, but that way of cutting (which cannot be done with a knife) almost invites unequal portions. While cutting with a straight line as is traditionally done cannot guarantee equal pieces, a division into 8 pieces can be done with a pretty good degree of accuracy.
Not only what @zenvelo said, but it’s not practical to have the “crust, no crust” cut from a practical standpoint. You’d have to stand there while people took the pizza and explain the “crust, no crust” choices. Unless you did, you’d have crust lovers taking slices that had no crust and vice versa. Also, there might be only a few that like crust but you’d have more slices with crust (or the opposite). The way of 12 traditional slices, triangle shaped, where everyone gets crust, would be more practical for people just grabbing slices without having to explain. Also, each slice would have crust and would be easy to cut.
I like a round pizza cut in squares. It allows for most variety of topping to crust to size choice.
@zenvelo , @jca , For any number of reasons, this cutting scheme is not going to work from a practical point of view. It is intended for abstract mathematical pizzas. I was hoping that at least some others would appreciate the cleverness of this non-obvious but still relatively simple way of dividing a circle into regions of the same shape and area in such a way that half of them are along the circumference.
To cut the diameter on a round pizza requires no more elaborate instrumentation than the box that it came in (assuming a square or rectangular box with at least one right-angle corner).
Every mathematician or engineer already knows that a circle can be halved by finding any two points along the circumference where an inscribed right angle projects an intersection. Cut from point to point, and you have cut a diameter.
If the pizza needs to be divided into quarters, then use the same technique to locate any other diameter. The point where the diameters intersect will be the center of the pizza. Place the edge of the box along the cut diameter, with the right angle located at the center, and you will have described the quartering cut. And so forth.
Very clever! Though I wonder how they account for uneven topping distribution? Because when the pizza pie pi gets more complicated than pepperoni, toppincs can add a whole new dimension to slice-selection!
@Soubresaut All mathematics profs eat cheese only pizza. Problem solved.
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