The Pizza Theorem

  • Published on Jun 6, 2018
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    *** LINKS ***
    The Pizza Theorem
    Mathematics Magazine, Volume 41, 1968: "Problem 660" by L.J. Upton, Solution by Michael Goldberg:
    Mathematics Magazine, Volume 67, 1994. "Proof without Words: Fair Allocation of a Pizza" by Larry Carter and Stan Wagon:
    Dividing Thin Crust, Calzones, and Stuffed Crust Pizzas:
    Exotic Mathematical Pizza Slicing:
    Infinite Families Of Monohedral Disk Tilings:
    Pizza Theorem Proof Without Words Calculator by Christian Lawson-Perfect:
    Vsauce Links
    Hosted, Produced, And Edited by Kevin Lieber
    Research And Writing by Matthew Tabor
    VFX By Eric Langlay
    Huge Thanks Paula Lieber
    Select Music By Jake Chudnow:

Comments • 3 167

  • Vsauce2
    Vsauce2  5 months ago +3674

    The book is perfectly fine. No damage whatsoever. Although it tastes delicious now...

    • Finnypainter 37
      Finnypainter 37 27 days ago

      I swear, I died inside once you put that book on the pizza!

    • Neekk0
      Neekk0 Month ago

      who cares about the book??? why would you ruin a perfectly fine pizza??

    • The bean Man
      The bean Man Month ago

      Legend has it the book is on the pizza and he is just using a different one

    • Ethan Dyson
      Ethan Dyson Month ago

      There is a special place in Hell for people who cut pizza like that.

    • TheSebas737
      TheSebas737 Month ago


  • The Summoner
    The Summoner Hour ago

    the first cuts resembles the flag of uk...

  • Ghostep_
    Ghostep_ Day ago

    0:57 Or one if it's me.

  • TheGEARGUY123
    TheGEARGUY123 5 days ago

    Sorry but it was hard to pay attention with that pizza just staring at me

  • Landon Dodson
    Landon Dodson 5 days ago

    Can you divide 0000000000000.1 by --------------------------00000000000000000.1

  • snow icecream
    snow icecream 7 days ago

    Can i have my pizza now?

  • Hello sir
    Hello sir 7 days ago

    Just cut the pizza in half.

  • mouse trance
    mouse trance 9 days ago

    humanns of earth are 22so very smart I aam fascinated by them :))

  • Lord Petar
    Lord Petar 12 days ago +1

    Looks like the logo of smash bros

  • Contor The Destructor
    Contor The Destructor 13 days ago

    now i want pizza

  • g r a n t
    g r a n t 13 days ago

    Hey, no fair! He got to eat a whole pizza by himself!

  • TheDiscoMole
    TheDiscoMole 13 days ago

    ill take the right half of that perfectly cut pizza pls

  • Connor Cook
    Connor Cook 14 days ago

    You can only cut it to the limit of two atoms, therefore, there is a limit.

  • Tanner Patton
    Tanner Patton 15 days ago +1

    You lost me at 3:08
    I’ve never had a problem understanding a TheXvid video and I’ve watched this part like 10 times...

    • Peter B
      Peter B 7 hours ago

      I don't think he really proves anything in this video. When he labels the second pizza he has some errors in which ones he capitalises and which one he hasn't, which doesn't help his explanation at all! But after wasting a couple hours of my life I think I understand.
      The idea of the proof is that in the second pizza (the stuck back together one) in the bottom left you have the same point which we cut from, and the same angles and sizes of the old slices are there, just they are now made up of different letters.
      What we should see is that the "old" a,c,e and g are all made up of lowercase letters, and likewise the "old" b,d,f and h are made up of capital letters. (you can do this if you swap the capitalisations of a,c and e) (He has the "old a" equal to h+E+A+C, and "old b" equal to D+e+a etc....) (see this img for my corrections: )
      This would mean that if we sum all of the lowercase letter areas up, this is equal to the old a+c+e+g, and if we sum the capital areas this is equal to the old b+d+f+h.
      But we know that the capital letter areas are equal to the lowercase letter areas, because that's how they were constructed (either the small areas are duplicated, or the big ones have a bit taken off and are split in half, by definition), so we have completed the proof.
      I've not read all of this paper, ( ) but I think it does the best job at explaining what's going on.

    • Nobody. green leader
      Nobody. green leader 8 days ago

      Lol same

  • Bagua Gaming
    Bagua Gaming 16 days ago

    I love how my YT stoped and it looked like he was about to shoot a pizza with a real gun

  • giacomo piseri
    giacomo piseri 16 days ago

    Everyone cringed for you putting the book on the pizza and then us italians laugh, cringed by how can you eat such a disgusting thing and call it pizza, literally te one in the video seems disgusting with all that cheese that seems like plastic, and everyobe in the comments talking about domino's and hawaiian pizza, THAT IS NOT PIZZA.

  • Bumpyburrito
    Bumpyburrito 16 days ago +1

    1:59 that really bugged me

  • Fer Kayaking
    Fer Kayaking 16 days ago +1

    your are a pizza nut!!! :-) Entertaining and interesting as always.

  • spook
    spook 16 days ago

    if someone cut a piece of pizza like this at a party i'm getting the knife

  • Clip Assassin
    Clip Assassin 17 days ago +1

    Can I now have the pizza please?

  • Plutonium2222
    Plutonium2222 17 days ago


  • Fredster Gaming
    Fredster Gaming 17 days ago +1

    Scientific Communism.

  • Cedrick James Eusebio
    Cedrick James Eusebio 17 days ago


  • Stupid japanese Learner

    V tomato sauce

  • Some Blob Demon
    Some Blob Demon 19 days ago

    Or you could just make multiple pizzas

  • Ziron of Time
    Ziron of Time 19 days ago +1

    Cut off the crusts

  • Jc Christ
    Jc Christ 19 days ago

    yea thats right divide it for two people but the most impotant thing is the ratio. the crust to body ratio.

  • Gameninhuis
    Gameninhuis 19 days ago

    now i am hungry

  • Justin Z.
    Justin Z. 19 days ago +1

    I thought he was gonna cut the pizza with the laser 😂

  • Clark Good
    Clark Good 19 days ago +3

    First Hawaii with the pineapple pizza, then San Francisco with the broccoli pizza, and now vsauce with the book pizza

  • IrllyNeEdaNAme
    IrllyNeEdaNAme 21 day ago

    *When you get the smallest peace and ask for a bigger one*
    Mom"this vid sais its even"

  • Shalinado :D
    Shalinado :D 21 day ago

    i dont understand the comments, i am qualified too stupid to be a human. someone do you speak my language?

    • Nobody. green leader
      Nobody. green leader 8 days ago


    • Shalinado :D
      Shalinado :D 21 day ago

      btw thank google translate for adding stupid language, then me writing this wouldnt have been possible

  • swite
    swite 21 day ago

    i fucking love vsauce

  • Coffeeh
    Coffeeh 21 day ago

    Poor pizza xD

  • Bob97 Ate a cookie
    Bob97 Ate a cookie 21 day ago

    This video makes me hungry.
    Hahaha!!! 3 days old pizza!

  • Turkish Mapper
    Turkish Mapper 22 days ago

    0:28 the pizza is cut in the shape of a weed leaf

  • SlimeElemental
    SlimeElemental 23 days ago

    I got a pizza ad on this.

  • Frank wo1fer
    Frank wo1fer 23 days ago

    Just eat the God damn pizza

  • :Devin!
    :Devin! 23 days ago

    I say screw it, and just eat it whole

  • Thomas Bigalow
    Thomas Bigalow 23 days ago

    Haters will say pineapple and/or books are not acceptable pizza toppings

    ALI ASIF CHOWDHURY 23 days ago

    i just want to know the title of the music at the end

  • Ay Boi
    Ay Boi 23 days ago

    Anything cut down the half point can feed 2 people

  • Heidi Barker
    Heidi Barker 23 days ago

    yeah but what if everyone wants a piece of crust?

  • Sk3ptic Surg3
    Sk3ptic Surg3 23 days ago

    Imma save you some time, feel free on having a bit more pizza compared to me. Idc

  • JCstock
    JCstock 24 days ago

    brb gunna make a pizza

  • Tommaso Vianello
    Tommaso Vianello 24 days ago

    2:00 just... no

  • Joe's Commenting Account

    Everyone is complaining about the book on the pizza but imagine rollin' up to a homie's house and he tryna cut a pizza that way

  • Justiney YT
    Justiney YT 24 days ago

    you didnt need to do math after u cut it like that if you wanted to share it with one other person.. just put 4 of the slices together from each side where u can see the cut down the middle... anyone could see that it was equal, besides the individual triangles

  • Duck Last_name
    Duck Last_name 24 days ago

    Can we just talk about how he put the book on the pizza?

  • XLOrange Ninja
    XLOrange Ninja 24 days ago

    That pizza is nowhere near a perfect circle. I got less pizza.

  • un_Poke h
    un_Poke h 24 days ago

    If you're making pizza cutting so hard, have the entire pizza. We're not friends anywhere.

  • Luis Crock123YT
    Luis Crock123YT 25 days ago

    im confusion

  • Gillatene47
    Gillatene47 25 days ago

    When the book touched the pizza, i flinched

  • trashmill
    trashmill 25 days ago

    As a german i'm triggered

  • Ω
    Ω 26 days ago

    Elbows off of THE *TABLE*

  • Ω
    Ω 26 days ago

    Elbows off of THE *TABLE*

  • Alice Trans Queen
    Alice Trans Queen 26 days ago

    That pizza gonna be cold by the time filming is done

  • Arkhitektz
    Arkhitektz 26 days ago

    damn this made me hungry....

  • Finnypainter 37
    Finnypainter 37 27 days ago

    Am I the only one who saw the word "fed" when he put the magnets on the pizza?

  • Anna Dyer
    Anna Dyer 27 days ago +1

    Did u just ummm

    Put ur book on ur pizza...?

  • Systemfehler
    Systemfehler 27 days ago

    Now... I... WANT...PIIIZZZZZZAAAAAA!!!!!!!

  • Doing Something Different

    My video 'The Brainy Panda' is also about taking non-brain objects as brains!

  • Junsi27 Chin
    Junsi27 Chin 27 days ago

    What's the use of this i can just make a math out of p*rn vid

  • medexamtoolsdotcom
    medexamtoolsdotcom 28 days ago

    Except what if your goal is not JUST to give them the same area, but the same amount of crust?

  • Mystic
    Mystic 28 days ago

    Me: Can I just eat the pizza already

  • Dabrien Williams/Hacker Cat

    4:21 I said "Youah Slice it." with him.

    Thats he 2nd sime i've done something like that today!! Or ever int his past month@! So yeah!

  • Dabrien Williams/Hacker Cat

    2:00 The cheese is dry people.

  • MythicalPhoenix19
    MythicalPhoenix19 28 days ago

    2:02 i felt physical pain when he put the book on the pizza.

  • Undeniable Loss
    Undeniable Loss 28 days ago

    I got a cauliflower pizza ad before this ._.

  • I wanna die
    I wanna die 28 days ago


  • Apples. that is all
    Apples. that is all 28 days ago

    well yea its going to be equal, he cut the pizza in half and then made more cuts. not degrading the video though. I like this one.

  • MR.Meat
    MR.Meat 28 days ago

    Just eat the f#$!ing pizza

  • Adam R
    Adam R 28 days ago

    I was physically harmed when he placed the book on that pizza. THINK OF THE OILS, MAN.

  • Astral Fire
    Astral Fire 28 days ago

    *Pie*-thagoras' Theorem
    *Pizza*-thagoras' Theorem

  • JamEpix
    JamEpix 29 days ago +1

    _Pizza Time._

  • trishia alvarado
    trishia alvarado 29 days ago

    Just buy another pizza lol

  • Arkaus
    Arkaus 29 days ago

    Nothing wrong with me gosshhhh 1:02

  • Kristopher Parnell
    Kristopher Parnell 29 days ago

    *places book on pizza*

  • Brown exe
    Brown exe 29 days ago +1

    But I want C R U S T mom

  • Sgt Wingman
    Sgt Wingman 29 days ago

    You ruined the pizza.

  • Fire /Phantom Forces
    Fire /Phantom Forces 29 days ago

    is this Like 3rd grade School lmao. and no im not in 3rd Lmfao.

  • ILoveKittens
    ILoveKittens 29 days ago

    Just eat that thing already!!! XD

  • Phillip Han
    Phillip Han 29 days ago

    Anyone else notice the FED?

  • Skeleton Bros
    Skeleton Bros 29 days ago


  • i cannot fly
    i cannot fly Month ago

    Who cuts a pizza like that?

    Vsauce2 does

  • Evo_Winters
    Evo_Winters Month ago

    What about square pizza? jk

  • Fawny Deer
    Fawny Deer Month ago

    But what about the crust?

    JAY PARMAR Month ago +1

    J U S T E A T T H A T D A M N P I Z Z A !

  • Abdurrahim Armagan
    Abdurrahim Armagan Month ago

    Did anybody else notice the sick starship enterprise pizza cutter?

  • Mikedoespapercraft YT

    I’ll have a #15 Burger King foot lettuce and a #8 book pizza

  • Mikedoespapercraft YT

    31 people for 1 pizza?
    That’s as normal as eating 1 tic tac at a time

  • Het Speelkwartiertje Slaat Terug

    Maybe that pizza will feed 1 person.. a 15 year old like me..

  • BeHappy--
    BeHappy-- Month ago

    The book.

  • Nyan Tun
    Nyan Tun Month ago

    hey man, can I have a slice of pizza?
    *gives smol piece
    ITS equaAL

  • Jharnekus
    Jharnekus Month ago


  • Sir Fish
    Sir Fish Month ago

    you gonna eat that?

  • w33d b3qr
    w33d b3qr Month ago

    c o n f u s e d

  • Bawi H.
    Bawi H. Month ago

    you lost me at pizza....

  • Tyler Hassey
    Tyler Hassey Month ago

    Can someone please make a fractal dive that looks like a pizza now?thanks

  • DyrianLightbringer
    DyrianLightbringer Month ago

    Everyone in the comments worrying about the book on the pizza, but nobody talking about how his pizza cutter can boldly go where no pizza cutter has gone before.