# On the Perfect Size for a PizzaOctober 18, 2013 11:29 PM   Subscribe

Eugenia Cheng of the School of Mathematics and Statistics, University of Sheffield has investigated the mathematical relationship between the size of a pizza and its ratio of topping to base (slpdf). We show that for a given recipe, it is not only the overall thickness of the pizza that is is affected by its size, but also this topping-to-base ratio.
posted by three blind mice (36 comments total) 8 users marked this as a favorite

"This study was funded by Pizza Express" (are they good? the name doesn't imply quality).
posted by el io at 11:40 PM on October 18, 2013

Acknowledgements
This study was funded by Pizza Express.

posted by hal_c_on at 11:41 PM on October 18, 2013

Sheffield?

Did you say "Sheffield"?

Regarding pizza?
posted by pompomtom at 11:49 PM on October 18, 2013 [3 favorites]

Quantities of topping and base. We assume that the same pizza recipe is being
used at all times, so that the total quantity of dough and total quantity of topping
remain constant
.

That is a really, really, really bad assumption OR this is the worst advertising Pizza Express will ever get. I worked at a pizza shop in college, where we had three different pizza sizes. Every size pizza had its own proportionally sized piece of dough (as measured by weight right after making the dough). For toppings, you'd cover the pizza to a certain depth or coverage proportion no matter what the size. Using the same amount of pepperoni on a 10" and a 16" pizza is just insane.
posted by LionIndex at 11:51 PM on October 18, 2013 [10 favorites]

Yeah, they make some questionable assumptions. I'm wondering about replicability....

Clearly, more research is needed.
posted by AsYouKnow Bob at 11:59 PM on October 18, 2013

First, assume a spherical pizza...
posted by Homeboy Trouble at 12:26 AM on October 19, 2013 [20 favorites]

this study was funded by pizza planet express

Good news everybody!
posted by Hicksu at 1:08 AM on October 19, 2013 [6 favorites]

As an English person I feel that I can say what everyone here must be thinking: Why in the name of ALL THAT IS GOOD IN THE WORLD are we letting English people run this project, fer chrissakes?
posted by ominous_paws at 1:12 AM on October 19, 2013 [2 favorites]

No no. The depth of the pan is a, and the radius is z. The formula is very simple.
posted by iotic at 1:16 AM on October 19, 2013 [12 favorites]

posted by Segundus at 1:36 AM on October 19, 2013 [4 favorites]

"This study was funded by Pizza Express" (are they good? the name doesn't imply quality).

For a chain, Pizza Express are very good, indeed the only UK pizza restaurant chain worth eating at in my view. And they don't do deep dish or serve chips (fries), which is a mark in their favour. Well, Polenta chips, whatever they are? (Menu)
posted by epo at 1:58 AM on October 19, 2013

iotic: "No no. The depth of the pan is a, and the radius is z. The formula is very simple"

Don't you EVEN
posted by DoctorFedora at 2:14 AM on October 19, 2013 [1 favorite]

This being a Pizza Express funded study, surely the operative question would be whether their pizza has shrunk over time. This would throw the formula out, if the constant is in fact not constant, no?
posted by dmt at 4:36 AM on October 19, 2013

Well, at least it wasn't funded by Papa John's, whose new "Mega Chocolate Chip Cookie" is not-so-mega. (So what would PJ know about size?)
posted by oneswellfoop at 4:44 AM on October 19, 2013

In my early morning fuzz I thought this research came out of the "University of Seinfeld", which for issues of this grave importance, made perfect sense.
posted by jeremias at 4:55 AM on October 19, 2013 [1 favorite]

Overthinking pizza has never been so delicious.
posted by elpapacito at 5:04 AM on October 19, 2013

That is a really, really, really bad assumption OR this is the worst advertising Pizza Express will ever get.

I think you're misinterpreting the study's premise - I'm pretty sure this is about "if your pizza recipe uses X amount of dough, what is the optimal radius to spread that dough to?"
posted by NMcCoy at 5:43 AM on October 19, 2013

Man, I've always wanted to drive I-55 between St. Louis and Chicago and plot mean pizza crust thickness as a function of distance.
posted by tss at 6:16 AM on October 19, 2013 [3 favorites]

This is really upsetting.

It uses a stupid model that obviously doesn't apply to real pizza.

They don't explain basic assumptions like that a "bite" is of fixed total volume, or dough thickness would be irrelevant. I think it would be of fixed total area; we can disagree but you have to explain it!

It claims to find the "perfect size for a pizza", but then doesn't perform any actual optimization, or even bother to graph anything as a function of size. That's because if you actually try to do some optimization, it quickly becomes obvious how silly this is.

The equation for topping density diverges at sqrt(15), or about 3.87, inches. Infinite topping density! Fine, this is because their model breaks here since the crust will occupy the whole surface. And away from this singularity it's monotonically decreasing. So the "perfect size for a pizza" is at worst "3.87 inches" or more charitably "as small as possible but not so small as to break our fake model".

This is obviously supposed to be "fun". I think maths is fun on its own. Why fake it? Yes, this is eye-catching, but is it really so hard to come up with a media-attracting "study" that actually holds up to anyone with high-school-level numeracy thinking about it for more than 30 seconds? And is it necessary to be directly and obviously misleading in the title of the paper?
posted by Pre-Taped Call In Show at 6:21 AM on October 19, 2013 [4 favorites]

For a chain, Pizza Express are very good, indeed the only UK pizza restaurant chain worth eating at in my view.

In the olden days, when they were limited to London, they used to also have pretty good live jazz. You don't get *that* at McDonalds.
posted by PeterMcDermott at 6:23 AM on October 19, 2013 [1 favorite]

This pizza smells like a press release designed to generate media Churnalism for some Pizza chain. With a topping for fresh bullshit and well seasoned by an academic who's got small payoff in exchange for devaluing academic research.
posted by Dr Ew at 6:28 AM on October 19, 2013

I was going to go all wop on this one (like, what? neopolitan style or sicilian style?), but then found that as humorous applied math it's pretty disappointing.

The main problem is that the title and premise of the paper is erroneous: there's no "perfect size" found--that would require some optimization with respect to a cost function, something which is not done. Instead, what was found was a scaling relationship showing the ratio of topping to crust as a function of pie radius. This scaling relationship is a monotonically decreasing function of radius on its valid domain, with a singularity on its left side, that asymptotically approaches the constant t/d as r goes to infinity. Thus, this approach cannot be used to find a "perfect" size.

So, I regretfully must recommend that this paper be rejected. Should the author secure additional funding from Pizza Express to continue this work, I'd recommend an optimization approach with cost function that includes at least some gastronomically-relevant factors related to oven physics.
posted by mondo dentro at 6:33 AM on October 19, 2013 [3 favorites]

Dr. Cheng is the Math-ster Chef--tortured food pix.
posted by Ideefixe at 6:58 AM on October 19, 2013 [2 favorites]

Woah. Great catch there, Ideefixe. So, this is likely part of resume building for a shot at a TV show, eh? Interesting idea. She'll have to do better than this example, though.
posted by mondo dentro at 7:04 AM on October 19, 2013

Is there an investigation of red pepper flakes making pizza taste 10X better?
posted by lineofsight at 8:44 AM on October 19, 2013 [1 favorite]

She also plays the Pi-ano
posted by Segundus at 8:49 AM on October 19, 2013

She already has a two-book deal with Profile. The first is Cakes, Custard and Category Theory, due out in 2015; the second will be about infinity and the eternal question of who ate all the pies.
posted by Segundus at 9:03 AM on October 19, 2013 [1 favorite]

Pizza Express is indeed good for pizzas and food, but you are paying for the quality (which can get expensive) and not the quality. It's also heck I can't find reference the most popular chain for divorced dads in the UK to take their kids when they have access to them.

Personally, I love their Sloppy Giueseppe (hot spiced beef, red onions, green peppers) pizza. But it's about a tenner - albeit fresh made in front of you - in the restaurant, or a fiver in the supermarkets, and in some supermarkets there are frequently offers e.g. 2 Pizza Express pizza's for £5.

On the paper itself; um, kinda thin (no pun intended) and short, though comforted that LaTex appears to still be in use.
posted by Wordshore at 9:59 AM on October 19, 2013

Also, yes, this is a book thing.
posted by Wordshore at 10:10 AM on October 19, 2013

Having written for a comic science radio show, I'm sort of thrilled at the perfect cream tea thing. The photos are not good, but she should certainly be a YouTube hit.
posted by Ideefixe at 10:30 AM on October 19, 2013

The premise is deeply flawed right out of the gate. Good pizza doesn't need toppings. If you put salt in the dough and spices in the sauce the pizza has it's own flavor and doesn't need to be corrupted with anything else. Most places here in Chicago refuse to go anywhere near the salt or the spices.
posted by bleep at 12:12 PM on October 19, 2013

With a topping for fresh bullshit and well seasoned by an academic who's got small payoff in exchange for devaluing academic research.

I'm certain that the field of pure mathematics will survive this travesty.
posted by Blazecock Pileon at 12:35 PM on October 19, 2013

Until Butcher King publishes a study on the optimum size of a hamburger. With graphs.
posted by happyroach at 12:39 PM on October 19, 2013

Until Butcher King publishes a study on the optimum size of a hamburger.

Ok, I admit to being ignorant of fast food chains in the US - but did you mean Burger King? Because if there is also a chain called Butcher King...well, I think that's just awesome and I would love to go and eat at one.
posted by nubs at 12:46 PM on October 19, 2013

Typically with these things they have to call a number of scientists until they find one willing to put their name to it...
posted by welovelife at 1:37 PM on October 19, 2013

The Pizza Express link suggests that this is another chapter in the great Pizza Express conspiracy, whereby everyone swears their pizzas have steadily been getting smaller and they assiduously deny it. Presumably this was defensive research, to be pulled out and issued as a press release if it is ever definitively proved that the pizzas have shrunk.
posted by Acheman at 2:56 AM on October 20, 2013

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