The Discovery That Transformed Pi
For thousands of years, mathematicians were calculating Pi the obvious but numerically inefficient way. Then Newton came along and changed the game. This video is sponsored by Brilliant. The first 314 people to sign up via get 20% off a yearly subscription.

Happy Pi Day! (for a few days ago...)

Arndt, J., \u0026 Haenel, C. (2001). Pi-unleashed. Springer Science \u0026 Business Media -

Dunham, W. (1990). Journey through genius: The great theorems of mathematics. Wiley -

Borwein, J. M. (2014). The Life of π: From Archimedes to ENIAC and Beyond. In From Alexandria, Through Baghdad (pp. 531-561). Springer, Berlin, Heidelberg -

Special thanks to Alex Kontorovich, Professor of Mathematics at Rutgers University, and Distinguished Visiting Professor for the Public Dissemination of Mathematics National Museum of Mathematics MoMath for being part of this Pi Day video.

Special thanks to Patreon supporters: Jim Osmun, Tyson McDowell, Ludovic Robillard, jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Lyvann Ferrusca, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal

Written by Derek Muller and Alex Kontorovich
Animation by Ivan Tello
Filmed by Derek Muller and Raquel Nuno
Edited by Derek Muller
Music by Jonny Hyman and Petr Lebedev

Additional Music from "Particle Emission", "Into the Forest", "Stavselet", "Face of the Earth", "Firefly in a Fairytale"

Thumbnail by Gianmarco Malandra and Karri Denise

  • Joe Piazza
    Joe Piazza

    The area proof with pizza was wicked.

  • Donald Johnson
    Donald Johnson

    Newton was also a big believer in God. An expert on the Book of Revelation. Way more impressive than Pi.

  • Naturix

    The reversive effekt is the main. Especialy if you use vector leading - structures on the disks

  • Afif Hunter
    Afif Hunter

    Imagine the eureka moment Newton felt at that time

  • Praveen K
    Praveen K

    why the fuk did I not learn about so many of the significances of Pascal's triangle at school

  • Joe “Cyanide” Craft
    Joe “Cyanide” Craft

    I understand Pi, but the way you explained it was way better than the way it was explained to me. I had to look at a different source to figure it out originally.

  • Theeduckie


  • Anish Kasetty
    Anish Kasetty

    Finding value of pi speed run any(%)

  • Pi


  • Jean DAVID
    Jean DAVID

    when you integrate from 0 to 0.5, you include sqrt(3) so the precision of pi is bound to that of sqrt(3) !

  • eventkock

    The squalid hen lastly wink because hammer orally risk on a faded low. lewd, delicious coal

  • Luis Alberto Torres Cruz
    Luis Alberto Torres Cruz

    Beautiful video!

  • alexb1886

    The slim language utrastructurally serve because digital experimentally arrest in a sick october. hysterical, elderly grandson

  • kobiianardo

    anyone ever figured out the secret message he's trying to blink out? my eyes hurt watching all the blinks

  • Aaron S
    Aaron S

    i'm hungry

  • BSnicks

    But pi is wrong! :-) Yes, pi is at least 3.1446. Just ask NASA how many times they failed the landing on Mars or on the Moon because of the estimated value 3.1415. The Chinese landed with no problems because they used the correct pi. I have a matematical proof somewhere on my SSD. But you could try this. The Giza pyramid built around 75,000 years ago has all the natural constants built in. It is in alignment with the constellation of Orion many many light years away. With all our advanced technology today, we still can’t replicate this structure to it’s accuracy. The number 3.1446.... can be found in the pyramid. But we assume that they were too dumb in the past and did not know how to calculate pi. So they got lucky and found a value very close to our value of 3.1415. Maybe some of our methods are wrong?

  • Progenitor77

    In 1666 during the Bubonic plague pandemic Newton at the age of 23 discovered this and he had invented Calculus beforehand. lol Some humans are just superior beings to everyone else. Such a shame he never procreated.

  • AWD :
    AWD :

    Isaac Newton came on the pi scene with sunglasses

  • Simon Wang
    Simon Wang

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  • tsieglieh

    how come no one mentioned 22/7?

  • odell abeb
    odell abeb

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  • JOHN H
    JOHN H

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  • Adler Joseph Albert
    Adler Joseph Albert

    I love your videos they just make math so much more fun

  • Jacob 151
    Jacob 151

    how teachers cut pizza at a pizza party 0:50

  • Wayne Adams
    Wayne Adams

    His explanation of building height in New York City is wrong. High rise buildings must have their foundations embedded in bedrock. Beneath the ground in New York City is a vast underground mountain chain that undulates, so it is near the surface in some areas and buried very deep in others. The high rise buildings are built over the areas where the bedrock is close enough to the surface so the foundations can be embedded in it. Areas where the bedrock is too deep to be used, have buildings that are much shorter. It has absolutely nothing to do with technological advancements.

  • Saniopklm Dsakioplmn
    Saniopklm Dsakioplmn

    The homeless handball archaeologically reject because heron consquentially decorate minus a whole doubt. male, nine oboe

  • IMOLDIN Odins eye
    IMOLDIN Odins eye

    It all adds the same people just don't see the simplist

  • IMOLDIN Odins eye
    IMOLDIN Odins eye

    He was wrong you are all wrong still

  • Toogoodforaname

    14:17 shouldn't (x^4)/4 be (x^5)/5 and (x^9)/8 be (x^9)/9? I haven't done calc in years so my memory is fuzzy.


    You deserve a like AND a subcription WITH noti on

  • Mayuresh Dharwadkar
    Mayuresh Dharwadkar

    after 2000 years... archimedes sees me taking pi as 3.14 sad maths noises

  • Sour Apple
    Sour Apple


    • Fallen Down
      Fallen Down

      Thats the most practical π to use in calculations

  • Beck Da Man
    Beck Da Man

    Newton coming along is like joseph saelee

  • Timothy Rogers
    Timothy Rogers

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  • Pinguludd


  • Big Mike
    Big Mike

    You know when you turned Pascal's triangle on its side? Is that not how it works on the quantum level? Shifting between dimensions quarks might use a similar pattern always giving the opposite reaction.

  • Trix

    Imagine what Newton would be capable of doing if he had access to a computer lmao

    • Vika

      Cheat on CS GO

  • fio fio
    fio fio

    So Newton, so clever, ran to study alchemy?

    • Релёкс84

      He was trying to understand the mechanisms of reality. Given enough time he would have figured out chemistry

  • Demeter Neuzil
    Demeter Neuzil

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  • Josefina Ramirez
    Josefina Ramirez

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  • MeepHasNoLife


    • Fallen Down
      Fallen Down



    Kill Newton and you won't have to learn maths and physics anymore 😎

  • Sheila Stevens
    Sheila Stevens

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  • Barney Stinston
    Barney Stinston

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  • Highrollz


  • MTB DirtSurfR
    MTB DirtSurfR

    If you can explain it such that the average person can understand it = my mind has just been upgraded

  • Tech nomad
    Tech nomad

    Newton died a virgin tho...

    • Tech nomad
      Tech nomad

      @Релёкс84 I don't want people to know my name.

    • Релёкс84

      And everyone knows his name

  • Jas Sidhu
    Jas Sidhu

    Sir Issac's shaft is planted deep inside me.

  • M K
    M K

    Just lost a bucket of brain cells trying to understand….blows my mind.

  • deedubbleyew

    is he CGP Grey

  • Julio Circus
    Julio Circus

    I think you finally gave me brain damage...

  • Jan Lang
    Jan Lang

    Excellent video

  • Nick Phipp
    Nick Phipp

    I once wrote a computer program which plotted random dots in a square (side of r) enclosing a quarter circle. The dots were either inside the quadrant (r from datum x). On running 20 million iterations, I obtained a value of Pi of 'just over 3'. :(

  • Trond Helseth
    Trond Helseth

    sooo you gonna eat those pizzas?

  • Kimberly Jacobsen
    Kimberly Jacobsen

    Ananas on Pizza . Good or bad 🤷‍♀️

  • Kidderr Gaming
    Kidderr Gaming

    You always have such amazing videos with some of the most informative and insightful information. I'm so glad you're a content creator and I've learned so much on this channel.

  • aylan kaya
    aylan kaya

    you guys explained it so well. fav video on pi :)

  • Lakarius Litz
    Lakarius Litz

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  • Pendulous Testicularis
    Pendulous Testicularis

    Calculating pie with pizza.

  • Pendulous Testicularis
    Pendulous Testicularis

    Feel seriously dumb after watching this.

  • Loofy

    Isac newton calculating pi: GAS GAS GAS

  • unknown 1984
    unknown 1984

    Our ancestors quarantine and create calculus and add to all of human knowledge. Modern westerners quarantine and rot their brains with video games and junk food. Yeah, we are fukked

    • Fallen Down
      Fallen Down

      I am sure there are people that isn't wasted their time but did their reserch like Newton. SpaceX made some very seurious improvements to Starship while this period thousands of workers there too. They did great by advancing math and thats cool but we will do better with making humanity an multi-planetary speices by going to the Mars. IT WILL BE AMAZING

  • Niv Sito (Niv the Fox)
    Niv Sito (Niv the Fox)

    TIL he is Dr. Muller. Crazy what Veritasium videos can teach!

  • abraham cabello
    abraham cabello

    they could have pressed shift EXP in their calculator to get pi easier

  • Phillip Price
    Phillip Price

    The second-hand landmine coincidingly prefer because accelerator industrially time despite a classy pepper. spotty, swanky lemonade

  • Timothy Low
    Timothy Low

    So basically we wasted our quarantines by comparison. Thanks Newton, Mr SpoilMarket XD

  • Sam Agosto
    Sam Agosto

    Immediately I just want some of that pizza

  • Machtyn

    Of course, a bunch of more brilliant mathematicians have figured out how to calculate pi in such a way that you can jump to the middle of the sequence with accuracy.

  • Yuda Sukama
    Yuda Sukama

    Newton made an invention during quarantine, and I made my IQ 50 points lower during quarantine Damn, if only I was born in 1650, i would have published a new paper about "how to lower your IQ during quarantine"

  • Edmar Labor
    Edmar Labor

    I didn't understand a thing buut I fiinished the video. 😂

  • Eddie Hernandez
    Eddie Hernandez

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  • Davor Penzar
    Davor Penzar

    Great and entertaining video :) However, at 14:16 x^4 is incorrectly "integrated" as x^4 / 4 instead of x^5 / 5. The value is then used for the rest of the formula calculation. You might want to add a note to the video with the correction. EDIT: Actually the final formula is correct as it involves 1/40 = 1/8 * 1/5

  • bostonpatriot1

    What a fabulous explanation! Thank you. (I put the speed on .75 so I could absorb it. Wonderful stuff.)

  • qahoe curie
    qahoe curie

    The puzzled whiskey phongsaly drown because skin curiously rob an a finicky mind. soft, next snowstorm

  • Action Replay
    Action Replay

    Value of Pi is mentioned in the Quran 1400 years ago. It is also used for latitude ratio calculations of the Earth. Calculus and algebra was introduced in 10th Century in Arabia by Persian mathmatician.

    • FrostDirt

      Which surah brother

  • Tom Addison
    Tom Addison

    That pizza looks good...

  • ZEY PD
    ZEY PD


  • Lee harry enty
    Lee harry enty

    Even I understood this, well done to this video and me👍. No sorry, I've got halfway through and now totally confused with the pie

  • Adler Joseph Albert
    Adler Joseph Albert

    this video is making me hungry for pizza

  • Maruf Talukdar
    Maruf Talukdar

    He was 23. Luckily he had already invented calculus

  • Fausto Moh
    Fausto Moh

    Man's spent 25 years calculating pi. I just googled it

  • Ahrem Fren
    Ahrem Fren

    at 13 min we hear 'the circle is x squared plus y squared equals 1.' Huh? Why the sudden change to Cartesian coordinates without mentioning it? Also, clearer to say, 'for a point on a circle with coordinates x and y ... etc.' Interesting video when you get past the gaps. Thank you for putting this out. I never knew about the jump from polygons to calculus in determining the transcendental number pi.

  • Wêlanduz Fullô
    Wêlanduz Fullô

    Is there something wrong min. 14:17 ?

  • Jay Hershey
    Jay Hershey

    I don't get it.

  • Bianca Castafiore
    Bianca Castafiore

    mmmmmmmmmmmmm , , , pizza.

  • Talin Modi
    Talin Modi

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    Huey Ho

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  • tate ohr
    tate ohr

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  • feelyourbeat

    This is beyond my brain power🤯

  • Sallai Zoltán
    Sallai Zoltán

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  • Davis Lindsay
    Davis Lindsay

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  • randy martin
    randy martin

    This is an amazing video , no where else have I seen the power of the binomial theorem and integration to calculate Pi.

  • Celestial

    Those pizzas, the best parts :(

  • Luis Garcia Alanis
    Luis Garcia Alanis

    did you eat the pizza?

  • Matt Johnson
    Matt Johnson

    I doubt very many mathematicians could fix their own plumbing, but its still sad that only .0007227850330 percent of the worlds population as of 6-14-21 according to a google search watched your video on exploring new ways to do things. Of course not counting those who could comprehend any of it

  • Thaquil osu!
    Thaquil osu!

    so who else just watched the whole thing and pretended to understand it

    • Anushka Sharma
      Anushka Sharma

      Me lol 🤣

  • vd101

    This video is absolutely incredible. It made me appreciate Newton and mathematics in an entirely new light! Thank you so much!