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 • 3 470

  • Vsauce2
    Vsauce2  7 months ago +4125

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

    • aapjes fan
      aapjes fan 13 days ago

      Tj I can’t believe you didn’t get upset over that

    • Jerrik Li
      Jerrik Li 24 days ago

      All i needed is for you to cut it into two pieces

    • The_Enderman SadAZaz999
      The_Enderman SadAZaz999 Month ago

      I WAS ABOUT TO SAY "2:05 you do know your book is covered in pizza now" XD

    • Finnypainter 37
      Finnypainter 37 2 months ago

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

    • Neekk0
      Neekk0 3 months ago

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

  • ejm116
    ejm116 22 hours ago

    I like pizza and math!

  • Dre Wolfshire
    Dre Wolfshire 3 days ago

    (Sees the first pizza)
    Super smash brothers Ultimate.

  • ruber president1o1
    ruber president1o1 4 days ago

    How to start a war just for few more grams of pica

  • Rainbow Thunder
    Rainbow Thunder 4 days ago

    *puts book on pizza*
    I'd still take that over pineapple thanks

  • Tobi wan Kanobi
    Tobi wan Kanobi 5 days ago

    Can I get one large pizza with pepperoni and extra ham

  • BlendFlix Animation
    BlendFlix Animation 5 days ago

    Bruh he just put the book on the damn pizza


    *world hunger has left the chat*

  • Aidan Chiranjiv Singh

    Just eat the pizza man! Oh and also did he....


  • Nyan Burrito
    Nyan Burrito 6 days ago

    In the second half of the video, the cutter looks exactly like the USS Enterprise from Star Trek.

  • Somerandomguybody
    Somerandomguybody 6 days ago

    This is so confusing. Of course your cut is perfectly half there’s one slice straight down the middle. Once that’s made, it doesn’t matter how you cut the rest....

  • April Trent
    April Trent 7 days ago +2

    2:00 Him: Puts book on pizza
    Me: Screams on the inside

  • ryanplestid
    ryanplestid 7 days ago

    Why on earth won't slices do? 360/n_people gives you the opening angle of each slice. You don't have to subdivide by a factor of 2 each time

  • Mitch Jones
    Mitch Jones 7 days ago

    Is that the enterprise 1701 as a pizza cutter cos I need that

    Live long and prosper 🖖

    JTCYE 8 days ago

    I got so disturbed when he put the book on the pizza

  • Thunderfire9
    Thunderfire9 8 days ago

    That’s pizza on the table is unsanitary. You wrote on the table with marker and now the pizza is touching it.

  • Asta kirizami
    Asta kirizami 9 days ago +1

    A Friend of Vsauce: hey our pizza slices aren't equal
    Vsauce: Hold my beer

  • GVG Everything
    GVG Everything 9 days ago

    You could do this, but you could also do digiorno

  • redneck gaming
    redneck gaming 10 days ago

    When you move the center it physically shortens it so it technicaly is not the same size

  • blocks
    blocks 10 days ago


  • StoneBucket124
    StoneBucket124 11 days ago

    did anyone else come down to the comments when he put the book on the pizza

  • I Don't Give A Fuck!
    I Don't Give A Fuck! 11 days ago +1

    I don't get it

  • Big Stinky Joanne
    Big Stinky Joanne 11 days ago +1

    Or you could just cut the pizza normally...

  • DiceyDie
    DiceyDie 11 days ago

    BuT wHat iF I wAnT tHe EdGE!?

  • Rasto Dibala
    Rasto Dibala 11 days ago

    I am hungry af.

  • Kaladin Stormblessed
    Kaladin Stormblessed 11 days ago

    That is one disgusting pizza.

  • Aaden  poops-alot
    Aaden poops-alot 12 days ago

    Book on pizza... this pizza will make you smarter
    Like this-
    2+2=4 -1=3
    Quickly done math

  • Jade
    Jade 13 days ago

    “Do you want your pizza cut in triangles or squares?”

  • aapjes fan
    aapjes fan 13 days ago

    Omg he had a Star Trek space ship as a pizza slicer

  • Tenzing Amji
    Tenzing Amji 13 days ago

    in the caption at the end it said this pizza is three days old. lol

  • Muttalip Sarıaslan
    Muttalip Sarıaslan 13 days ago

    Our Pizza、Our Proof.

    Communism intensifies.

  • Karaoke King
    Karaoke King 13 days ago

    1:02 whats wrong with this person

  • Brody Hays
    Brody Hays 13 days ago

    It’s 2 in the morning how did I get here

  • Ghetto Mar
    Ghetto Mar 13 days ago


  • memeulie
    memeulie 13 days ago

    That pizza dusty

  • - LyteZ -
    - LyteZ - 14 days ago +1

    As quoted from sponge bob, “We only serve food here sir”

  • This Stop Motions
    This Stop Motions 14 days ago +1

    Kevin! Vsauce here! Oh wait...

  • Nonificality
    Nonificality 14 days ago +1

    My last brain cells may have died

  • GabGamingUltra 123
    GabGamingUltra 123 14 days ago +1

    Why was the pizza cut formed like Smash?



    2:34 boi dats the world of light hard mode pic
    Edit its easier to see at 2:51

  • Jay the RioteerFN
    Jay the RioteerFN 14 days ago

    You dare cut a pizza like this

  • 100 subs no vids !
    100 subs no vids ! 14 days ago


  • Guillaume Paniagua
    Guillaume Paniagua 15 days ago

    Stop playing with food please.

  • Member of Chara Defence Squad

    Shape of that pizza cutter tho:)

  • CAJ
    CAJ 15 days ago

    I dont get it

  • meshumo
    meshumo 16 days ago

    You should've eaten it before it got cold.

  • I want to die
    I want to die 16 days ago +1

    How dare you dishonour the great and mighty pizza

  • Cara Stark
    Cara Stark 16 days ago

    1:01maybe they're lactoseintolerant
    I probably spelt that wrong
    Took me forever to pause the video at the right time

  • Supscribe 4
    Supscribe 4 16 days ago

    0:28 what are you talking about. There is a cut right down the center. Of course there are two equal amounts of pizza for the two persons.

  • Rosie Griffiths
    Rosie Griffiths 16 days ago

    It’s a frickin pizza. Just eat it 😂😂😂

  • TheGolden Apple
    TheGolden Apple 16 days ago

    So you try to tell me if you would choose the 4 smallest slices and I would take the 4 biggest slices we would still eat the same amount of pizza?

  • HarveyDTV
    HarveyDTV 16 days ago

    Where’s my pizza

  • Reagan McNearney
    Reagan McNearney 16 days ago

    Just casually sets the book on the pizza

  • Gaming Wolf
    Gaming Wolf 16 days ago

    Why did I laugh so hard when you put the book on the pizza?

  • Eli 579
    Eli 579 16 days ago

    Is this how freddy cuts his pizza

  • Dr. Awkward
    Dr. Awkward 17 days ago

    Who else did it disturb that he put the book on the pizza?

  • Edwin is Awesome
    Edwin is Awesome 17 days ago

    You can just buy more pizza

  • Sherrinford Stockholm
    Sherrinford Stockholm 17 days ago

    2:13 omg don't put it on the pizza

  • Pära
    Pära 17 days ago

    You really just. Put that book right on that pizza.

  • BLOBz Rules
    BLOBz Rules 17 days ago

    Seriously? No pizza puns???

  • Codename: Xelda
    Codename: Xelda 17 days ago

    By cutting a pizza into a peenwheel. Lol 1:15

  • Codename: Xelda
    Codename: Xelda 17 days ago

    It got cold while he was measuring it

  • Hello sir
    Hello sir 17 days ago

    2:08 (
    *(announcement) I repeat this is not a drill! He put the book on the pizza!*
    (Citizen) “What?! Call 911!!!!!!!!!”
    (Someone calls the police) (other citizen): “THE POLICE ARE ON THEIR WAY!!!!” *police siren* (officer): “WE NEED BACKUP! THIS IS A CODE RED EMERGENCY!!!!!” *backup arrives* (officer): “CHECK FOR ANY SURVIVORS!!!!” *The entire town died... Thanks, Kevin*

  • Hello sir
    Hello sir 17 days ago

    One of my many pet peeves:
    When an item that is not a dish or utensil touches food. When that book and protractor touched the pizza, I disliked the video! So don’t do that again, and all is good.

  • Hello sir
    Hello sir 17 days ago

    Or you can just *EAT IT ALL >:D*

  • lol XD
    lol XD 17 days ago


  • Jammy Beast
    Jammy Beast 17 days ago

    What if you dont like crust

  • Darren D. MacDonald
    Darren D. MacDonald 18 days ago

    Yo, you gonna finish that pizza...

  • James Rhile
    James Rhile 18 days ago

    Pizza looks like the smash logo

  • Rebecca George
    Rebecca George 18 days ago

    But... The crust...

  • TopHatKitty
    TopHatKitty 18 days ago

    It's not that deep when you realize it's just because it's cut in half and then those halves are just cut weird.

  • SuperCreativeUsername
    SuperCreativeUsername 19 days ago

    One pizza feed four people? I’d pass out by the time I finish the cheese

  • Slime Productionz
    Slime Productionz 19 days ago

    ...okay, can I have a slice now?

  • Mega Meta
    Mega Meta 19 days ago

    It’s now cold

  • Michael Feliciano
    Michael Feliciano 20 days ago +2

    Why did you have to put the book on the pizza 🍕🍕🍕🍕

  • Simply Robert
    Simply Robert 21 day ago

    For my birthday I'm cuttin my pizza in the smash logo

  • Tuesday's Taco
    Tuesday's Taco 21 day ago

    stop playing with your food and just eat it

  • Ethan Chin
    Ethan Chin 21 day ago

    you suk

  • VermiCulo
    VermiCulo 21 day ago

    *That's a horrible looking pizza*

  • Agent Delta
    Agent Delta 22 days ago

    The edge of a pizza isnt the same as the middle
    Cutting a pizza like this doesnt just make you look like a smart arse, but also doeant equally distribute the differant parts of the pizza

  • FlameLavaPlayz Roblox
    FlameLavaPlayz Roblox 22 days ago

    Me:dad can i have my leftover pizza
    Me:Can You Cut It Into Monohedral Disk Tiles?

  • Isaiah Camacho
    Isaiah Camacho 22 days ago

    Ur Making The Pizza Cold So I Will Not Eat It >:(

  • Child Does MATH
    Child Does MATH 23 days ago

    Anybody else saw that the E and e are the smallest bit of pizza

  • Loren Paghasian
    Loren Paghasian 23 days ago

    I dont get it but pizza

    LIVE EVIL 24 days ago

    That pizza looks nasty

  • Dakota Weverink
    Dakota Weverink 24 days ago

    2:00 just puts the book on top of the pizza

  • Louis Herrera
    Louis Herrera 24 days ago

    Shut up nerrrrd

  • FaTyl
    FaTyl 24 days ago

    I can smell this video

  • Sara A
    Sara A 24 days ago

    im so confused why is this even a question you cut a diameter on the weird sliced one and the pizza's equal on both sides of that cut wtf

  • Appocalypse
    Appocalypse 25 days ago

    Love the USS Enterprise pizza cutter!!

  • Samuel B. St-Pierre
    Samuel B. St-Pierre 25 days ago

    That pizza must be cold af

  • Jaden Alfonzo Agpaoa
    Jaden Alfonzo Agpaoa 25 days ago

    1:16 what if the crust was stuffed crust

  • Kitty Commits oof
    Kitty Commits oof 25 days ago

    Nooooo my half of the pizza is cold because of your long explanation oh wait so as your half ha

  • Sinper_YT
    Sinper_YT 25 days ago

    I thought I were the only one who loves books on my pizza😍

  • Crazy Gamer Kids
    Crazy Gamer Kids 26 days ago

    Solid vid 9/10

  • Username Taken
    Username Taken 26 days ago

    How about we just order another damn pizza

  • Rathan Muruganantham
    Rathan Muruganantham 26 days ago

    What is wrong with this person?

  • Matthew Read
    Matthew Read 26 days ago

    But everyone doesn’t get the same amount of crust.