Pizza Rule

I once taught private lessons in math on calculating the area of a circle and I wanted to show the students how much cheaper per area a larger pizza is. So we of course got the diameters of pizzas from their favorite restaurant and started calculating. Then we found out that the normal sized pizza was actually the cheapest per area. It wasn‘t quite what we expected, but a very good math lesson for the attendees nonetheless: The owner lost money, because they were bad at maths.

You didn't consider the crust ratio, did you?
The crust tends to be a consistent width, so it represents a greater portion of a smaller pizza, shrinking the bit most people are there for.
...but hey, if you love the crust just as much, more power to ya!
- Keeping the total pizza volume fixed, many smaller pizzas also means more boxes.
I have an app for that, put the price and diameter of different pizzas and it says what's the best one price wise.
Did you take into account that the crust takes away area from the "filling"? Because me and my husband also once did the math (not sure if we were frugal, bored or broke) and it all came down on whether you eat/enjoy the crust or not
- Crust is part of the pizza. That's what dipping sauces are for.

But the 2 12” pizzas have more crust, so it depends what you prefer.

I’m wholly in the pizza centre and fuck the crust camp. But for those who like the crust…

You're meant to eat the crust, not fuck it, that might be where you're going wrong
- You're meant to eat the crust, not fuck it
  Really? Guess now I know why everyone has been looking at me funny after the company pizza party 🤔
I mean I like crust but who's out here looking for a higher crust ratio?
Shit man, I'm a crust guy but hate paying more for less...
You sort of ruined my life now.
Merry x-mas you bastard

Pizza π

The volume of a pizza with a radius of "z" and a height of "a" is πz²a, or pizza
- Very nice :)

If you let the radius be Z, then you can find the area of a pizza with a simple formula:

Pi * Z * Z = A

I wish I could award you with fake Internet points.
I love this

What's an inch?

A measure of length equal to 1440 twips, 3 barleycorns or 1/7920th of a furlong.
Not enough
- dang

Importantly, it also has a different crust-to-center ratio, which - depending on your taste - could be a reason to go for less pizza.

given a choice, i usually go with larger pizzas for crispy thin crust (also cut those in squares); and smaller ones for 'deep dish' or pan, where there isn't really an outside 'crust'.

you can fit more pineapples on the one 18 inch pizza

9 is more than 2 times 4

But… it’s twice as many slices!

OK, but with the 2 pizzas on the right, I get twice as many slices of salami.

Well IRL that wouldn't be the case since the pepperoni is the same size on a 12 vs 18 inch, therefore more pepperoni slices on the 18 inch due to the larger area
But each slice of salami on the left has more than twice as much salami as each slice of salami on the right.
There's no cheating math.

yeah, but
C_1 = pi * d = 3,14 * 18 = 56,52
C_2 = pi * d * 2 = 3,14 * 12 * 2 = 75,36

so the smaller ones have 50% more crust and are therefor more delicious.

You can compare areas with just r^2 you don't even need pi. So the math is easy.

A pizza is larger than two of another just before it hits 1.5 times the radius (sqrt 2 times, to be exact, about 1.41). So if the radius is 1.5 times bigger, like in the OP, you always know it's more than twice the area.