Pizza physics (New York-style) – Colm Kelleher

Translator: Andrea McDonough
Reviewer: Bedirhan Cinar Pretty much everyone loves eating pizza, but it can be a messy business. Pizza is soft and bendable. So how can you stop
all that cheese from falling off? You might know some tricks: you can use two hands —
not so classy, or you can use a paper plate and allow only the tip
of the pizza to peek out. There’s one other trick, though: holding the crust, you can sort
of fold the slice down the middle. Now the tip of the pizza
isn’t falling over, and you can eat it without getting
tomato sauce all over yourself or accidentally biting off
some of that paper plate. But why should the tip stay up
just because you bent the crust? To understand this,
you need to know two things: a little bit about the math
of curved shapes and a little about the physics
of thin sheets. First, the math. Suppose I have a flat sheet
made out of rubber. It’s really thin and bendable,
so it’s easy to roll into a cylinder. I don’t need to stretch
the sheet at all, just bend it. This property where one shape
can be transformed into another without stretching or crumpling,
is called isometry. A mathematician would say that a flat
sheet is isometric to a cylinder. But not all shapes are isometric. If I try to turn my flat sheet
into part of a sphere, there’s no way I can do it. You can check this for yourself, by trying to fit a flat sheet
of paper onto a soccer ball without stretching or crumpling the paper. It’s just not possible. So a mathematician would say that a flat sheet and a sphere
aren’t isometric. There’s one more familiar
shape that isn’t isometric to any of the shapes we’ve seen
so far: a potato chip. Potato chip shapes
aren’t isometric to flat sheets. If you want to get a flat piece of rubber
into the shape of a potato chip, you need to stretch it —
not just bend it, but stretch it as well. So, that’s the math. Not so hard, right? Now for the physics. It can be summed up in one sentence: Thin sheets are easy to bend
but hard to stretch. This is really important. Thin sheets are easy to bend
but hard to stretch. Remember when we rolled
our flat sheet of rubber into a cylinder? That wasn’t hard, right? But imagine how hard
you’d have pull on the sheet to increase its area by 10 percent. It would be pretty difficult. The point is that bending a thin sheet takes a relatively small amount of force, but stretching or crumbling
a thin sheet is much harder. Now, finally, we get to talk about pizza. Suppose you go down to the pizzeria
and buy yourself a slice. You pick it up from the crust,
first, without doing the fold. Because of gravity,
the slice bends downwards. Pizza is pretty thin, after all, and we know that thin sheets
are easy to bend. You can’t get it in your mouth, cheese and tomato sauce dripping
everywhere — it’s a big mess. So you fold the crust. When you do, you force the pizza
into something like a taco shape. That’s not hard to do —
after all, this shape is isometric to the original pizza, which was flat. But imagine what would happen
if the pizza were to droop down while you’re bending it. Now it looks like a droopy taco. And what does a droopy taco
look like? A potato chip! But we know that potato chips are not
isometric to flat pieces of rubber or flat pizzas, and that means that in order
to get into the shape it’s in now, the slice of pizza had to stretch. Since the pizza is thin,
this takes a lot of force, compared to the amount of force it takes to bend the pizza in the first place. So, what’s the conclusion? When you fold the pizza at the crust, you make it into a shape where a lot
of force is needed to bend the tip down. Often gravity isn’t strong enough
to provide this force. That was kind of a lot of information, so let’s do a quick backwards recap. When pizza is folded at the crust, gravity isn’t strong enough
to bend the tip. Why? Because stretching a pizza is hard. And to bend the tip downwards,
the pizza would have to stretch, because the shape the pizza would be in, the droopy taco shape, isn’t isometric
to the original flat pizza. Why? Because of math. As the pizza example shows,
we can learn a lot by looking at the mathematical properties
of different shapes. And it’s especially nice when those shapes
happen to be pizza slices.

100 thoughts on “Pizza physics (New York-style) – Colm Kelleher

  1. Why was this illustrated like an art-house John Waters-type horror film
    I don't need to be emotionally scarred to learn why pizza is a physical marvel

  2. I have always bent the pizza to prevent it from flopping and at parties when I see kids flop a pizza on their face I teach them the trick. They think I am a genius!

  3. For the mathematical formality: You can calculate the Weingarten map at any point on the 2D surface. Intuitively this is the matrix corresponding to the change in direction of the normal vector at every point in the surface. (Normal being the vector upwards perpendicular to the surface.) For instance, if your point is at the bottom of a "u"-shaped curve, and as you move to the right the normal vector will point backwards.

    The Weingarten map is a matrix. The eigenvalues of the matrix are the principal curvature with the direction of the curvature given by the eigenvectors. If you place your surface like a sheet of paper on a table and define the normal to be in the upwards direction, a principal curvature of > 0 means it curves like a "u", while a principal curvature of < 0 means it curves like a "n". So a potato chip will have principal curvatures of opposite signs, both nonzero, and a ball will have principal curvatures both of the same sign, both nonzero. The side of a cylinder will have one of its principal curvatures nonzero (as it curves around the circumference) and the other principal curvature zero (as it is flat going up the side of the cylinder).

    The determinant of the Weingarten map (ie the product of eigenvalues) is the Gaussian curvature. It turns out all surfaces isometric to a flat surface have Gaussian curvature 0. That's what you can curve a sheet of paper (both principal curvatures are 0) into the sides of a cylinder without stretching the paper, but you can't turn it into the surface of a ball or a potato chip. That's also why the pizza trick works.

  4. You still can complicate it more if you like. Jesus…
    It's because when you fold it you are adding more support against gravity because the sides are pointing upwards now.
    and if you don't take that for an answer why should I take yours when the bent pizza shouldn't be isometric with the unbent because it's 3d not 2d you know..

  5. The pizza shaped food they serve outside a 50 mile radius of Chicago should not be called Pizza.  The only real pizza is in Chicago.

  6. I will never look at potato chips the same way ever again, they shall now from this moment forth be called DROOPY TACOS!!
    I will never look at pizza the same way again.. that face was downright creepy XD

  7. about folding pizza in half i knew it when i was like 5 i just folded in half bc its easyer to hold 😉 i am a smart kido 😀

  8. Why do westerners waste so much food while making these videos? I've noticed this everywhere in North America and Europe. It's such a culture shock to me.

  9. This is a terrible video. It doesn't actually explain anything. It just says "because math." It never actually went into the physics or math. It just said a folded slice can't droop…untrue. I've folded slices of pizza and had the tip droop down. Explain that one, slice.

  10. I've a doubt.. A skull is eating pizza. Does that mean that eating pizza is actually bad for the health?? You know kind of analogy or metaphor

  11. I heard that voice on the street one day, looked over and low and behold it was indeed a pizza talking. He was eaten

  12. I understood why it worked before, I couldn’t have explained it though. The recap was really good, I was a little lost, and it was exactly what I needed to get back

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