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., & Haenel, C. (2001). Pi-unleashed. Springer Science & 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


  • MannyXVIII
    MannyXVIIIOrë më parë

    Albert Szent-Györgyi once said: "Discovery is simply seeing what everyone else has seen - but thinking what no-one else has thought."

  • Roozyj
    RoozyjOrë më parë

    Me: clicks on a video about calculating pi Also me: Wow, there's so much math in this video!

  • Brian Ginis
    Brian Ginis4 orë më parë

    Alex and Derek, At the 14:15 mark of this video, possibly the “magic” and “fireworks” proved an ample distraction, as it appears that the third term [in the brackets] of the new equation has both an errant exponent and denominator [(x^4)/4 should be (x^5)/5], while the fifth term has an errant denominator [(x^9)/8 should be (x^9)/9]. Math is the purest form of beauty, and this collaborative video is surely a treasure. I hope you take no umbrage in the addressing of this apparent, albeit minor, discrepancy. One question: By adding both the obverse and third dimension to Pascal’s work, has Newton not effectively altered the resultant geometric shape away from that of a simple “triangle” and to more of a point-to-point bipyramid of sorts? ⌲◅ Thank you for all your videos. Your enthusiasm on such a wide variety of subject matter is refreshing, thought-provoking, contagious and most appreciated!

  • Ivana Notyers
    Ivana Notyers6 orë më parë

    Just shave. Please. Both of you.

  • Karthik Vigneshwar
    Karthik Vigneshwar7 orë më parë

    Big fan of this channel and all the videos! This new format of interviewing experts in the field about really interesting topics is amazing. Looking forward to more of these!!

    MANIVANNAN S7 orë më parë

    Mistake: @ 14:20 use x pow(9) / 9 not /8

  • LongJourneys
    LongJourneys9 orë më parë

    God, now I want some pizza.

    GRAVES STAND II9 orë më parë


  • flawedsociety
    flawedsociety10 orë më parë

    I heard English spoken, clearly. But I have no idea what was said.

  • M N Dan
    M N Dan11 orë më parë

    *Who was thinking that Newton could calculate all these complex things but why unable to find immediate cure for plague!*

  • Clayton Root
    Clayton Root12 orë më parë

    Holy crap. My mind just BLEW UP! Haven't experienced anything like this since Calculus.

  • Fernando Jose Profis
    Fernando Jose Profis14 orë më parë

    Seems like I need very much to revisit my mathematic book.

  • Dan Martin
    Dan Martin14 orë më parë

    History is not real and Newton and his ideas presented here are a fallacy.

  • Sp1cuLe
    Sp1cuLe17 orë më parë

    where is the pizza mukbang now :3 the discussion just made me hungry 😂😁🤣

  • Chien Yang
    Chien Yang18 orë më parë

    Newton revolutionized mathematics while in quarantine, so I am waiting to see what will come out of the current quatentine.

  • Dark Matter
    Dark Matter18 orë më parë

    Are you gonna eat that or not ?

  • Alice Wight
    Alice Wight20 orë më parë

    3:48 "our committe's line" instead of "Archimede's line" Whoever you paid to do your captions is an idiot.

  • Daniel Paulson
    Daniel Paulson20 orë më parë

    You guys are racist! Lol

  • SammySuSuu


    8 orë më parë

    Ching chong ding dong its aint racist if you hate all race equally

  • Pacaj Albert
    Pacaj Albert21 orë më parë

    Malo kto pochopil a mohol pochopiť pred 2000 rokmi ťažko váhu ľahkú kde sa to dostal do Európy o niekoľko 1000 rokov neskôr

  • Kofi Afriyie
    Kofi Afriyie23 orë më parë

    Man if you don't want the pizza give it to me I am hungry 🙁😅

  • Aden Ven
    Aden VenDitë më parë

    18:28 ℼ*100 rounded to the closest whole person 👍

  • Photo Rezeptor
    Photo RezeptorDitë më parë


  • Dineshsing Girase
    Dineshsing GiraseDitë më parë

    Do you also know that in ancient India around 500 CE, the mathematician/astronomer named Aryabhata calculated the correct value of the Pi to 3 decimal places! He also mentioned about irrationality of the Pi then which was only discovered in 1761 by Lambert. It's sad you did not even mention of such a great India mathematician Aryabhata in context with Pi. Anyways, it's a nice video and I appreciate your work.

  • LucasakaChubby
    LucasakaChubbyDitë më parë

    My math teacher actually used this video to explain to us

  • Jon Deaux
    Jon DeauxDitë më parë

    So this was all to get FREE pizza????

  • Hussain Alhashem
    Hussain AlhashemDitë më parë

    Newton 23 and quarantining = invents new math Me 36 and quarantining = barely figure out that I need to wash my groceries

  • Hussain Alhashem
    Hussain AlhashemDitë më parë

    Opputonity missed to post this video on 3.14

  • Jake Wild
    Jake WildDitë më parë

    Note: the size of buildings in Manhatan are directly related to the geology. Search a cross section of the Manhattan geology and reference it to the city scape. The Engineering implications become clear at that point.

  • To Mo
    To MoDitë më parë

    My head hurts.

  • Dennis Chen
    Dennis ChenDitë më parë

    When you are 23 years old and are able to have this insane level of insight, can you imagine what that's like.

  • Merhawi Tesfaye
    Merhawi TesfayeDitë më parë

    I just fall in love with Newton

  • Nilabhro Sinha
    Nilabhro SinhaDitë më parë

    tum toh bade heavy driver ho beteee..........

  • Aaru mani kattu
    Aaru mani kattuDitë më parë

    What about Ramanujan

  • Boris Ljevar
    Boris LjevarDitë më parë

    I'm just wondering, if in van Ceulen time there was cloud computing and he could do this in no time using brute force (multi-CPU distributed algorithms), would Newton ever come up with this idea brilliant idea? I.e. why would he spend a huge intellectual effort to do something manually that a computer farm can do in a fraction of a second? One could turn this question around and ask, how many brilliant ideas are we missing today (by not even trying to develop and understand) just because we have this brute force computing power at our disposal? My fear is that by increasingly relying on advanced technologies, such as machine learning, artificial intelligence, and generative design, we are in danger of going down the rabbit hole of competence without comprehension.

  • Amanullah Kariapper
    Amanullah KariapperDitë më parë

    Fantastic work!

  • Diamon
    DiamonDitë më parë

    Tryna watch this without having done factorials is pain. Gotta come back to this

  • Paul Byrne
    Paul Byrne2 ditë më parë

    I see a problem...If we use a method for calculating PI that is an approximation, then the resulting calculation will always be wrong. Example: If we create a series of polygons, say 2^100, it will NEVER be correct because there will always errors in the Arc Length. So to say that PI is an infinite series, is only true because we are using the wrong technique. The problem with Newton's method is that it uses Cube Root of 3 which does not exist. So the method is still not correct because it is using techniques that are wrong. So how can we calculate the value of PI using techniques that are NOT approximation techniques. Any time we use an approximation to calculate anything, the resulting answer will also be an approximation.

  • Pranav1
    Pranav12 ditë më parë

    Pity on the people who disliked this video(Since they have no brain).

  • Vegeta Ejji
    Vegeta Ejji2 ditë më parë

    Can you also explain the Method By Ramanujan to finding the value of pie... pls

  • Thunder
    Thunder2 ditë më parë

    And there's me who haven’t done any maths related to pi yet..

  • Naimul Haq
    Naimul Haq2 ditë më parë


  • Ishaan Garud
    Ishaan Garud2 ditë më parë

    can anyone believe I am just 13 years old , I still understood everything I also know PYTHON, JAVA and C

  • 00UncommonSense00
    00UncommonSense002 ditë më parë

    I am from Indiana. Pi is 3.2. That makes things much simpler

  • SozeyTozey
    SozeyTozey2 ditë më parë

    I like to watch these videos and pretend I understand what’s going on

  • bausHuck
    bausHuck2 ditë më parë

    I love your videos. As soon as I think I understand something and think I am sorta smart, you change the gear to insane and I feel lost. But I still learn. Thanks for all your hard work to make the world smarter. I just wish there were a way to get kids interested in this stuff.

  • shivam kashyap
    shivam kashyap2 ditë më parë

    Newton is extremely genius 😵😵

  • Mostafizur Rahman
    Mostafizur Rahman2 ditë më parë

    man this thing blew my mind!

  • John Biard
    John Biard2 ditë më parë

    what's with the pineapple on the pizza? That was so distracting that I missed the main points

  • Arsenix -
    Arsenix -2 ditë më parë

    This video helped me to understand my classes more easily, I love this explication

  • Jose Gonzalez de Durana
    Jose Gonzalez de Durana2 ditë më parë

    A nice exercise that could be used to motivate students in the study of Calculus. I have seen that there are a couple of typos: at minute 14:19 after integrating the previous expression, where it says x^4/4 should be x^5/5 and where it says x^9/8 should be x^9/9. 

  • cappel
    cappel2 ditë më parë

    I don't get it.

  • Asaf Shalev
    Asaf Shalev2 ditë më parë

    I am sorry, but the abomination with the pineapple there is not a pizza, making this video invalid.

  • Duke Yin
    Duke Yin2 ditë më parë

    Woa. This math professor's background was a virtual one! So he put his actual office pic as his background. I did not notice until almost the end lol

  • Jim DeCamp
    Jim DeCamp2 ditë më parë

    The Germans (at least some Germans at some times) call pi "die ludolphsche Zahl" in honor of Ludolph van Ceulen. Archimedes did more than just invent the polygon method, he provided a recursion formula for length of a side of a doubled polygon, greatly facilitating calculation.

  • PiecesOfNature
    PiecesOfNature2 ditë më parë

    Not sure if I want pie or pizza now :/

  • Tim H
    Tim H2 ditë më parë

    at 14:17 isn't the x^4 suppose to become a (x^5)/5 ?

  • Calkimchi
    Calkimchi2 ditë më parë

    I would have understood pi so quickly if I had learned it with pizzas like this

  • Average Alcohol Enjoyer
    Average Alcohol Enjoyer3 ditë më parë

    Derek never ends to surprise me

  • Rob Finch
    Rob Finch3 ditë më parë

    I don`t like pizza. Will it work with apple pi?

  • D Daniel
    D Daniel3 ditë më parë

    Dr. Alex. What do you think about using vortex mathematics in conjunction with the calculation of pi?

  • D Daniel

    D Daniel

    2 ditë më parë

    @MuffinsAPlenty The only reason why I gave you a zero by the way is because you were so easy to dismiss VBM. And your definition of VBM although that may be your interpretation, comparatively speaks of someone who has more angst or charged emotional feelings about the topic and you allow that to override logic in your definition. This is not a troll nor am I denigrating you however as a person of knowledge who works of people of greater knowledge than I can truly take apart the inaccuracies of your definition. I’m glad you spoke up though thank you for your response. I’m curious where do you draw your information from? Watching ALthe videos?

  • D Daniel

    D Daniel

    2 ditë më parë

    @MuffinsAPlenty Some of the elements in what you said might be considered as true, the other elements seems like to me anyway that you have yet to fully understand what Vortex Based Mathematics is about. I personally know many top scholars in the subject, who would strongly differ from what you say. If 1 is yes and 0 is no, then my friend you receive a zero for your answer.😉

  • MuffinsAPlenty


    2 ditë më parë

    "Vortex mathematics" is not mathematics in any meaningful sense. "Vortex mathematics" is continuously getting astounded by the following theorem and thinking that somehow it holds all the secrets of the universe: *Theorem.* If n is a multiple of 9, then the sum of the digits (in base ten) of n is a multiple of 9. This is a special case of a more general theorem: *Theorem.* Let b be an integer greater than 1. If n is a multiple of b-1, then the sum of the digits (in base b) of n is a multiple of b-1.

  • Zaraspe, Bong Jr. G
    Zaraspe, Bong Jr. G3 ditë më parë


  • Zaraspe, Bong Jr. G

    Zaraspe, Bong Jr. G

    3 ditë më parë

    Thank me later

  • Ahmed Syed
    Ahmed Syed3 ditë më parë

    Newton’s genius always gives me goosebumps.

  • Subhadeep Das
    Subhadeep Das3 ditë më parë

    Everyone - "Nobody is perfect in this world" Newton - "just watch and learn

  • Black Burgundy
    Black Burgundy3 ditë më parë

    Kind of funny to imagine dream’s speed run music while Isaac was doing his calculations

  • takhe tabyo
    takhe tabyo3 ditë më parë

    wow.......even thoe i didn't understand anything

  • Ajayi Pelumi
    Ajayi Pelumi3 ditë më parë

    Wait wait wait..I think I actually just learned more about circles in the first 2 minutes lol..and I'm a college student...studying engineering...damn...

  • Wakssbm
    Wakssbm3 ditë më parë

    Why does every amazing discoveries are always by the same narrow group of people?

  • FallNorth
    FallNorth3 ditë më parë

    The poor Dutch guy who did all that work then had it superceded by a much better method will be spinning in his grave. At least he'll be able to accurately calculate how many radians per second.

  • FallNorth
    FallNorth3 ditë më parë

    @7:45, In Newton's day, EVERYONE knew binomial theorem. I keep saying education is getting more and more dumbed down, this is just further evidence!

  • Deus X. Machina Animé
    Deus X. Machina Animé3 ditë më parë

    Isaac Newton delivers like a “G”. See! (Menulog!) 😜 Love this video!

  • Jonathan
    Jonathan3 ditë më parë

    they never get to the point...

  • Gary Brunner
    Gary Brunner3 ditë më parë

    I continue to be amazed that if we know the exact diameter of a circle, we can never know the exact area or the exact circumference.

  • black star
    black star3 ditë më parë

    The discovery that transformed Pi? APPLES!!They make the best Pi

  • Kalash Sarode
    Kalash Sarode3 ditë më parë

    So like, you first rotated the rotated Mandelbrot set, and now you rotated pascals triangle. These things are illegally mind blowing.

    KETAN CHAUHAN3 ditë më parë

    math's so beautiful

  • Venkat Babu
    Venkat Babu3 ditë më parë

    Pascal's triangle is a way of parallels twisted pair. You can do anything with parallels. If you take a thick wire the accuracy is less for pi twist.

  • Yanki 122
    Yanki 1223 ditë më parë

    Ancient mathematics: Calculating the number to more than a quantillion sides. Me: Drops 22/7 like a bauss.

  • Yanki 122

    Yanki 122

    Ditë më parë

    @FBI ok Sir

  • FBI


    Ditë më parë

    That ain’t Pi tho. That’s like 3.141414141414...

  • Greezy
    Greezy3 ditë më parë

    Interesting enough, "22/7" is the closest you will get to pi (with whole numbers) In numerology, 22 is the master builder number, 7 is often related to God, because G is the 7th letter of the alphabet.

  • Greezy


    2 ditë më parë

    @MuffinsAPlenty true i should have been more specific

  • MuffinsAPlenty


    2 ditë më parë

    22/7 is, by no means, the closest you can get to pi with a fraction. An even better rational approximation is 355/113. Now, it is true that 22/7 is a _very good_ rational approximation of pi with small denominator. It's the best rational approximation of pi you can get with the denominator being a positive integer less than 10, for instance, but you can always find better and better approximations if you're willing to allow larger denominators. 355/113 was known to Zǔ Chōngzhī from China in the 400's CE.

  • Mason Wheeler
    Mason Wheeler3 ditë më parë

    5:04: "The year was 1666." [Scene shows overhead shot of a quaint, medieval-looking villa... with power lines clearly visible] 😂

  • Isbaahu Dawuda
    Isbaahu Dawuda3 ditë më parë

    Very sad 😂🤣💔💔 pi did not pass through Africa .

  • Arjun Ghosh
    Arjun Ghosh3 ditë më parë

    Newton in quarentine calculating pi Me in quarentine watching how Newton calculated pi during quarentine

  • Mr Picky
    Mr Picky4 ditë më parë

    the way he tortures' that poor pizza is just unacceptable!

  • Fiskie
    Fiskie4 ditë më parë

    Being so arrogant and inconsiderate to buy seven big pizzas for something like this and to smile at it. Honestly its disgusting.

  • Michael Melling
    Michael Melling4 ditë më parë

    I'm so stupid I can't figure out how to get the Internet overlords to stop shadow banning me as well as all of the other clever and unfair things they do to me. And it's been going on since 2017.

  • Yash
    Yash4 ditë më parë

    This is one of the most interesting video i have ever scene

  • No One
    No One4 ditë më parë

    Why when the hexagon in the circle with sides of length 1 makes the diameter of the circle 2?

  • sealand000
    sealand0004 ditë më parë

    Something came out of his quarantine.

  • animewatcha
    animewatcha4 ditë më parë

    anyone come into here thinking Star Trek Discovery came in and changed Pi somehow?

  • Joe Don
    Joe Don4 ditë më parë

    Finding a way to calculate Pi is a life and death problem.

  • majorgeeek
    majorgeeek4 ditë më parë

    Newtons method did not transform Pi it simply is a quicker way of approximating Pi

  • Diego M. Rodriguez
    Diego M. Rodriguez4 ditë më parë

    4:40 Ludolph Van Ceulen had the number inscribed in his tombstone, but in one part the inscription is written as 3,1413926... The put a 3 instead of a 5! In the circle, heads down, just after "EN MINDER ALS".

  • Ferro Faza
    Ferro Faza4 ditë më parë

    im gonna tell my kids this is professor x

  • DeepDiveDisco
    DeepDiveDisco4 ditë më parë

    No wonder no one ever figured this out until Newton.

  • Jochenvds
    Jochenvds4 ditë më parë

    Hexagons are the bestagons

  • Thiago Jacinto
    Thiago Jacinto4 ditë më parë

    I swear you’re talking about planets

  • WaapRepeat
    WaapRepeat4 ditë më parë

    Veritasium is saving humanity

  • Minton Barry
    Minton Barry4 ditë më parë


  • Lionel Messi
    Lionel Messi4 ditë më parë

    Newton is SUCH a legend. The greatest intellect the world has ever seen, in my opinion.

  • Andrew Marcus
    Andrew Marcus4 ditë më parë

    "Pie" is related to pizza? Is pizza a pie?

  • ezequiel garcia
    ezequiel garcia4 ditë më parë

    Hi there! Thank you really much, this is a great video. I would like to know 2 things. If there is anyone that could answer me I would be pleased. First of all where does Leibniz came into part here (I'm not team Leibniz, i'm just asking). Second, as a infinite sum of rational numbers we got an irrational number as a result, what does it means.

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