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 comments on “Pizza physics (New York-style) – Colm Kelleher”

  1. Mozey ™ says:

    ooor y'know just eat it with 2 haands

  2. Charlie C says:

    What the fuck am I watching.

  3. MegaMGstudios says:

    this video is so red

  4. Coxinha Doce says:

    or you could just eat with knife and fork. (we eat pizza like this here in Brazil)

  5. Jessica Lewis says:

    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

  6. Samuel Tibbitts says:

    the lighting in this video made me uncomfortable

  7. Sagar Kapasi says:

    It's Super Awkward To See A Skull Eating Pizza Under Green Lighting

  8. Neil Shen says:

    Why? because of "meth!"

  9. Nicholas Rising says:

    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!

  10. Reila Z says:

    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.

  11. CarpetCleaner says:

    Nice video. Except for that annoying contrast that killed my eyes.

  12. Señor WoofWoof says:

    Vsauce anyone?

  13. Randall Stephens says:

    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..

  14. Anny Zou says:

    never have i thought that i would be taught about math by a slice of pizza

  15. Parth Patel says:

    Why does this even matter?

  16. Kalpna Saxena says:

    Because math, duh.

  17. Jess Lee says:

    How u ruin pizza , bring math into it 😒

  18. Seafoamfucker says:

    why not use a knife and a fork? its common in europe

  19. paru bantawa says:

    so does pizza make you fat or smart

  20. Adwitiya Dixit says:

    I can almost imagine him covering Gorillaz.
    "All my life….."

  21. Dave Atlas says:

    I hate pizza

  22. pereiramariana35 says:

    you get an A+ for pizza, and because math, and because im batman

  23. Matt M. says:

    🅱️ut is it 🅱️ONELESS?

  24. Logan Perry says:

    or you could put your thumb on the tip

  25. Sarah L says:

    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.

  26. Quality Content says:

    Now I'm hungry.

  27. Angelina Matta says:

    you are yummy 🤤🍕

  28. Caged Egg says:

    boring obvious simple and pointless

  29. Seiban says:

    Why does this look like it was filmed under a blacklight?

  30. Joshua Nelson says:

    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

  31. Shakes McTremens says:

    I call shenanigans — what do Scots know about pizza ffs?

  32. David Lee says:

    Because of Maths

  33. Alpha Killer says:

    So tacos?

  34. Alpha Killer says:


  35. Habojel says:

    Stop staring at the pizza, don't let it burn your braincells, jUsT eAt It!-

  36. Haruyuki Miyoshi says:

    Pizza Steve? Is that you?

  37. Garl Vinland says:

    What has happened to TED-ED?

  38. Stupidt says:

    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 😀

  39. Artistic Lion says:

    I already knew this was the right way to eat a pizza

  40. Synx says:

    i wanna eat

  41. Ray says:

    Lol I've always just used one hand with my thumb extended forwards to stop the pizza from drooping.

  42. Konstantin Zlatarev says:

    Its angers me to see pizza being man handled with such disrespect

  43. curt nonan says:

    ok im just gonna eat the pizza.

  44. Abdurrehman says:

    i just feel hungry

  45. Jacob Casha says:

    Rip pizzas

  46. Eric Pal says:

    What is up with lighting?! Holy cow it looks like it’s gonna be the next “don’t big me I’m scared” video lol

  47. Creative Writer says:

    Actually, I don't like Pizza.

  48. spartan says:

    If you pizza is to floppy my answer is get better pizza

  49. Bg Fg says:

    Droopy Tacos

  50. seven 215 says:

    Pizzas were harmed in the making of this video

  51. HO LAM YIU says:

    Damnit. Now I want PIZZA

  52. A B says:

    I understand the theory explained, but what is the question to be answerd?

  53. A Human says:

    R.I.P talking pizza
    eaten by hungry physicist
    we will all remember you for teaching us how to eat pizza

  54. HeyItzRane says:

    How to make a shape of a potato chip with a flat sheet: Find a flat potato chip. The sheet is already flat. XD

  55. Augusto Undead says:

    I watched this.
    Because pizza is nice

  56. Naval Kishore says:


  57. abababbb says:

    I love his accent

  58. Topy says:

    I find it creepy af :v

  59. Naomi Geraldine says:

    but how about pasta dough, you can strech and bend it, right?

  60. foram doshi says:

    That pizza is horrible. How about a dominoes?

  61. Honeybunnyハニーバニー says:

    I love pizza and I always use a napkin to make myself clean and you forgot to mention that.

  62. Saleem umar says:

    This is both creepy 😲and mind blowing 👍

  63. F A says:

    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.

  64. Daniel Tan says:

    He got a Pizza accent

  65. WuzNab says:

    I can smell sound now.
    My third eye has opened. 😳

  66. cxx says:

    "Can I have the pizza now?"

  67. Nicholas C. says:

    do i hear an irish accent?

  68. Eyal282 says:

  69. Christien Sebastien says:

    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.

  70. Kevin Le says:

    The only useful video

  71. Korasi says:

    Being British and calling a football “soccer ball” is shameful, even if your viewers are 90% American

  72. Cherry Noble says:

    Eat the pizza & you consume its knowledge.

  73. Jeffrey over9000 says:

    Watched this video while eating pizza.

  74. JamesTheFox says:

    He is talking about cannabilisome

  75. Ahmad Idris says:

    Why? Why? Why?


  76. ヨーソローちゃん_17 says:

    I'll keep this in mind

  77. Demir Tekayak says:

    Hey there, Mr. Pizza

  78. Misty Matchy says:

    That "potato chip" was a Pringle.
    Pringles aren't chips.
    They're "Crisps."

  79. Praw says:

    I have never seen anyone hold pizza like that

  80. Ranjeeta Gupta says:

    Feel sad when pizza was getting stretched😖.

  81. william jackson says:

    The one thing that bothered me this whole video was the color

  82. Sleepy Dog says:

    70% of the vid time is a team of ppl filming a single person holding a pizza slice

  83. thetruth isalie says:

    I didn't know that math was delicious

  84. Mythiasorcio says:

    I always order droopy täcos.

  85. retosius says:


  86. Midhun m s says:

    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

  87. Average Johnson says:

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

  88. Will Bill says:

    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

  89. Autumn Winds says:

    This was such a fun video! Thank you for posting it!

  90. Anim MusicTM says:

    STOP FREAKING BENDING IT!!!!!! …. it makes me hungry

  91. ᖇᗩ乙0229 says:

    My physics teacher showed up with this video

  92. bhaskar joyita says:

    Like and love it.sooooooooòoooooooogood

  93. Monica Velasquez says:

    "Why? Because of math" honestly my algebra teacher

  94. Keith West says:

    The most annoying part is that when the talking pizza is talking, it's voice isn't muffled or anything.

  95. Julianna D says:

    Ted-ed + Don't hug me I'm scared = ^

  96. le Derpium says:

    Conspiracy: Pringles are actually tacos

  97. Derpy Woodoo says:

    You could also just hold it balanced on your 5 fingers with your thumb by the tip and the other 4 by the crust. This way, you don't get all of the grease funnelling down to the tip like you would if you were to fold it in half as suggested in this video. Great math though!

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