STUMP » Articles » Math Stupidity: Comparing Pizzas and What's Important » 11 January 2019, 07:36

Where Stu & MP spout off about everything.

Math Stupidity: Comparing Pizzas and What's Important  


11 January 2019, 07:36

There is certain kind of clickbait that can catch me, and some math-related stupidity can.

So, I saw the following via Powerline: Putting the Pi in pies: Twitter user stuns the internet with math that proves one 18-inch pizza has more in it than TWO 12-inch helpings

The theory was posted by U.S.-based Twitter user @fermatslibrary
Supported by a graphic, the theory proves that one 18 inch pizza is better value than two 12 inch pizzas
Since it was posted, the tweet has received almost 1,500 comments and a total of 60,000 likes
It has also been retweeted 25,000 times, as people try to spread the word
Some users are baffled by the theory, claiming that it cannot be true
Last month, an article in the New York Post revealed that it is better value to order individual pizza slices rather than an entire pie

So. This makes the “news”. But not the 80% fundedness myth.

This is what John Hinderaker had to say about this:

I am often baffled as to how so many of our fellow citizens can fail to understand basic facts of politics and economics. It is sobering to be reminded that many of them are stumped by the size of a pizza. I think liberals must understand this better than we do, which is why they generally appeal to emotion rather than reason.

Look, this is not a Democrat vs. Republican issue. I mean not only the pizza but emotion vs. reason. Republican politicians also use emotions, too, but they’re different emotive thrusts.

And that’s not even my point.


Here is my video take:


I’ve had calculus students who claimed not to know the area of a circle. I wrote about this back in 2000:

Some people complain that calculator use in math classes is a crutch. I disagree – they can be very helpful. However, when I see current freshmen in first semester calculus classes, I realize that often calculators are not only crutches given to people who can’t use their legs but crutches given to those who also can’t use their arms. Students come into Calculus, with perfectly fine SAT scores, unable to solve algebraic equations and unable to graph lines. Giving these students graphing calculators which also can do symbolic math helps noone. For when they come to a related rates problem which states “You have a circle whose radius is expanding at the rate of 2 centimeters per second. How fast is its area growing when the radius is a meter?” they will complain to the TA “But we didn’t know what the area of a circle is!” (this happened to me in
the first class I TAed.)

These are students, having had Calculus the previous year in high school, classes which went all the way through integrals, who have the slightest idea of a derivative.

Math education hasn’t much improved since then (and my argument is that the main reason it hasn’t improved is that the teachers generally don’t understand the math they are supposed to be teaching)… but don’t feel bad if you don’t know how to compute the area of a circle or don’t know calculus. Heck, I used to help other actuaries with their kids’ calculus homework, because I was the only person who actually remembered it. Actuaries do not directly use calculus very much, though it underlies many of our models.

But actuaries understand how the numbers interact. We have some complicated stuff, and it’s okay that non-actuaries don’t understand all the fiddly bits.

A lot of the math you learned in school probably isn’t (directly) useful to you, and that’s even true for numerate folks. I’ve forgotten a lot of not only “school” math (by which, for me, that means grad school math), but also chemistry, literature, etc. That’s okay. It’s even okay that there is some math you didn’t learn (I probably remember a lot of math that many/most of you readers never learned… nor never knew existed. Even if you have a math degree… math is hyuuuge.)

But you do need to understand that certain numbers are bigger than other numbers, etc.

That you don’t know that an 18-inch pizza has bigger area than two 12-inch pizzas is no big deal.

If you don’t know that 81 is bigger than 72, then you have a problem.

The math you need to understand to get through life, for most folks, is not really complicated. This stuff is arithmetic + a few other things, and it doesn’t even include algebra.


There is the math you need to know as an individual.

- Taxes
- Interest rates on loans
- How savings compound over time, and what are realistic, and unrealistic, outcomes
- The trade-off between uncertainty in results and paying for insurance against those results

To be able to understand some of these, you mainly need to add, subtract, multiply, and divide, and understand what those mean.

And you really need to understand percentages.

Given what I blog about, I assume most people coming here are numerate on this level. I talk about numbers at that level a lot. I rarely do anything terribly complicated math-wise here.

But the vast majority of people aren’t reading my blog. And the vast majority of people would rather not think about numbers in the first place. I understand that.

If you know somebody who needs help with math, a great FREE resource is Khan Academy — I highly highly recommend it.


So, while few people are listening to me, more people are watching, reading, and listening to various news folks.

What math do the journalists really need to understand?

They need to understand:

- how basic statistics work: mean, median, mode, standard deviation, and sample sizes
- the difference between percentage increases and percentage point increases
- The distinction between rates and absolute amounts
- how to read a simple income statement and balance sheet (and what the differences are)
- how units work in general (like miles per hour, etc.)

There is more, but I’m talking about some very basic ideas.

Here is some basic math for journalists

An exhortation from 2010 for journalists to understand numbers more:

CAIRO—I tell my students that in addition to English they should learn two more languages: an in-demand foreign tongue, and statistics.

Studying Chinese or Hindi is a great move for an aspiring reporter, but numbers are the true global language. Journalists who can amass and interpret data can cover more of the world in a short time than reporters who just spill prose based on what they see.

And yet this harmful dichotomy persists. It is still common to hear a journalist woefully mumble, or even gleefully declare, that they’re “not a math person.” Plenty of college journalism programs, including the one in which I teach, don’t require students to take a statistics course. Some young people even gravitate toward journalism because they believe there won’t be any math involved.
Fortunately for journalists who aren’t “math people,” the latest WikiLeaks bombshell sprayed shards of diplomatic cables, which, if one reads English, can be combed and discussed. But if they don’t have basic knowledge of descriptive and inferential statistics, what will reporters be able to do with even moderately complex datasets dumped on WikiLeaks? Sadly little.
Journalists can’t do everything, and it’s easy for media critics to enumerate all the things that modern reporters must be. I’m not even full of my own medicine: I’ve never taken a macroeconomics course, and I know that my reporting has at times been less substantive as a result.

But statistics is too pressing a global language for journalists to neglect. Statistically untrained journalists are watchdogs without olfactory cells; they’ll catch wrongdoing when it’s visible, but they lack the skill to sniff a sour deal.

I have talked with some very numerate journalists, and they do tend to gravitate to the business and finance areas. Yes, there are a few journalists covering public finance (such as Mary Williams Walsh), but they are only a few who exist.

There are loads of publicly available data, such as via the Public Plans Database or Open the Books. Local journalists… if they understood the numbers, could use these tools to find stories. Do they know what to look for? Is it really news that you have a bunch of people making over $100,000/year in certain positions? (You’d have to compare against comparable positions elsewhere. It doesn’t shock me, for example, that doctors at public university hospitals get paid a lot. What do you think these sorts of specialists get paid at private hospitals?)

A lot of the public finance coverage is driven by both events (annual budgeting) and by press releases (yes, I receive these, so I know what ‘stories driven by some non-profit org pushing out a press release’ looks like.)

But wouldn’t it be nice if an investigative journalist knew how to investigate financials and find the stories on their own?

Now back to silliness.


I love pizza crust (meaning the edges, without toppings). So I want to maximize my crust take.

Now, I could get complicated and do a “area of pizza crust” comparison (okay, I will do that at the very end, but not quite yet). But let’s keep it simple and measure the crust simply by the circumference of the circles.

While the area of a circle is pi times the radius squared (and the radius is half the diameter), the circumference is simply pi times the diameter.

Circumference of an 18-inch pizza: pi * 18
Circumference of two 12-inch pizzas: 2 * pi * 12 = pi * 24

24 is larger than 18.



Okay, let’s get super fancy. Crust isn’t one-dimensional (which is what circumference measures). It has its own width. Now, I like really crusty pizzas, so let’s say that crust (the part without toppings) is 1 inch thick on pizzas of any size.

So the crust is really the difference of the whole pizza area minus a pizza one inch smaller in radius.

So the crust for an 18 inch pizza -> radius = 9 inch => difference between area of a 9-inch-radius circle and an 8-inch radius circle =

pi * (9^2 – 8^2) = pi * (81 – 64) = 17pi

For the 12 inch pizza -> 6 inch radius -> difference between area of 6-inch-radius pizza and 5-inch radius pizza

pi * (6^2 – 5^2) = pi * (36-25) = 11pi

So two of them is 22pi


But yes, the 18-inch pizza has more area overall.

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