## 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 brilliant.org/veritasium get 20% off a yearly subscription.

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

References:

Arndt, J., & Haenel, C. (2001). Pi-unleashed. Springer Science & Business Media - ve42.co/Arndt2001

Dunham, W. (1990). Journey through genius: The great theorems of mathematics. Wiley - ve42.co/Dunham1990

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 - ve42.co/Borwein2012

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 epidemicsound.com "Particle Emission", "Into the Forest", "Stavselet", "Face of the Earth", "Firefly in a Fairytale"

Thumbnail by Gianmarco Malandra and Karri Denise

## Komente

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

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

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!

Just shave. Please. Both of you.

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!!

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

God, now I want some pizza.

artofimposturefilm

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

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

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

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

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

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

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

Are you gonna eat that or not ?

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

You guys are racist! Lol

## SammySuSuu

## 8 orë më parë

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

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

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

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

EAT THE BLOODY PIZZA!

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.

My math teacher actually used this video to explain to us

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

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

Opputonity missed to post this video on 3.14

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.

My head hurts.

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

I just fall in love with Newton

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

What about Ramanujan

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.

Fantastic work!

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

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.

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

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

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

Archimedes

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

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

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

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.

Newton is extremely genius 😵😵

man this thing blew my mind!

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

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

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. ￼

I don't get it.

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

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

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.

Not sure if I want pie or pizza now :/

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

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

Derek never ends to surprise me

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

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

## 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

## 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.

4:28-4:30

## Zaraspe, Bong Jr. G

## 3 ditë më parë

Thank me later

Newton’s genius always gives me goosebumps.

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

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

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

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...

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

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.

@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!

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

they never get to the point...

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.

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

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

math's so beautiful

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.

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

## Yanki 122

## Ditë më parë

@FBI ok Sir

## FBI

## Ditë më parë

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

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.

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

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

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

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

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

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.

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

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

Something came out of his quarantine.

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

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

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

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".

im gonna tell my kids this is professor x

No wonder no one ever figured this out until Newton.

Hexagons are the bestagons

I swear you’re talking about planets

Veritasium is saving humanity

.

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

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

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.