# 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

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Transforming how to calculate Pi, inventing Calculus and creating the law's for Gravity all in one lockdown. I still need to put that shelf up.

What about Madhava contribution? Madhava series...

They might as well be speaking a different language. 🥴

That last little twist just blew my mind.

Don’t you just love it when a virus breaks out and you find a life changing discovery?

12:22 uhh is that library behind him fake? seems to be a green screen

Pie equals a circle. Stop over thinking this fact.

im in 8th grade and i have never heard about that triangle thing. surely u would think that i would know it by now especially in algebra class

@Veritasium typo at 14:20 , after integration, the X^4 should have become X^5

Pi/2=90° which is one fourth of a circle

Now we have to learn different laws , theorems , postulate in order to find something we could invent 😂

What if each room could fit an infinite number of people

Veritasium, I have to know, where did you get those pizzas? They looked delicious.

Invitation code shahjamal111 For Pi Network

What a great video. Really mind blowing what deductive reasoning can do.

thank you for this ... really appreciate it ...

Newton revolutionized math in 5 different ways doing his isolation. What have you done since Covid started?

nice, now Im hungry :(

Who else is proud of themselves to follow the video all the way to the pizzas? 🍕🍕🍕

Ludolph van Ceulen: I spent my 25 years to calculate 35 digits of π Newton: Hold my APPLE🍎

So just asking.. *For the big round ass, is that infinite number also applied?* 😀

3.14 is not all the precision that we need, it's pretty clear that the autor is not an engineer 😃

was parker on time ? PIZZA TIME !

didn't know tom morello was into pi

Thank you! It's really helpful.

What would happen if n is a complex number?

The expansion of the universe is time. Without expansion you don't have infinite, the same reason why you can always ad a decimel point. You can do this because of the expansion of the universe. In the future, future civilizations won't understand theorys like the big bang because they can't see evidence of it. Could be the same reason we don't understand what was before the big bang. Because their is no data before that moment

Dark energy is also time

I'm not gonna pretend I'm smart enough to understand all of this

No pizzas were harmed in the making of this video*

Pi are square but square is in.

Im an indian , and i hate self proclaim proud petty indians who brag to feel superior (fill their insecurities) , just becuz someone with a great mind lived 2000 yrs ago within 2000 km radius from his home . None of the guys here said "Our European Newton "

I like pi it taste good.

pineapple pizza -> UNSUBSCRIBED.

Wonderful! I don't understand how newton caught that

Why did you circumsise that pizza?

Awsome Channel - evan the Advertising is interesting. Thats the way youtube should be. Thanks

Last night I was thinking how the circle's area formula been made? and youtube show this in my recommendation😁

Geez lol. And what did WE all do during lockdown?

I hate Math and I watched this in full attention... that's how good Derek's videos are 😅

Don't waste pizzas

didn't know that Newton do speedruns

This is the type of ingenious stuff you can come up with if you don't spend all day thinking about getting tail. I'll never be a genius.

PI pi full form is P=perfect people - I involve inside information... that is meaning of pi.. now.. new reason create pi meaning.. )( ..it is create three meaning.. 3-6-9 9 is top art 3 is first art 6 is last art.. three in one meaning 3in1 3=1...1=3 3+3(1)' 3+3+1 =7 ........let's gooooooooooo pi create the human-beings pi=picture of living beings-living things p=peace living create I=involved non living living thing non living thing pi art is give reason of whole beings walking in exists...place.. pi solve Bsqure now.. 2 hand finger=10 +namaste namaste is=1 10+1=11 2 legs=10 2legs=10 2hand=10 20...teen endinnn. meditation stage..1 hole body.. 7 chakra meditation time 108 reason of life.. 1(0)+8 =9 than~0 so reason know 0-9 value of 0 to 9 in count..around ....so times is..human arts stand to pose of namaste... 10finger of hand 10legs pose of namaste 1 hole body is 1 10+10+1+1 22 # then 22/7 Bsquare proofs Health.. I am SOS-303 save our soul 333 save soul spirits S.S.S i am processing human civilization.. 8 types.. 8wonder... Healthy Body healthy life processing healthy habit good habit-good result healthy life style daily routine.. food vegetable fruits.. water and medicine.. cure all disease.. 100% vegetarian life process make disease resistant. .100 out of hundred guaranteed.. mortals soul and spirits immortal life.. ..big mestrious reason.. aquatic life processing.. starting ULTRA arts.. land arts and forest arts is Anti-clock ice land is aromatic arts human civiliZation is ULTIMATE ARTIFICAL POWER ENERGY=1. .. the 3 arts is exist world and another world.. exist world=○ another world= - middle world=| ................. exist world is= Time another world is =LiGht=1,speed=1 middle world is=machine Artifical.. AVATAR..... A star.. I am star BoY.. goinin shine Diomond.. like diamond in the sky.. but I am earth son. I am PLUTO BOY.. COMin earth to burn to find the reason of life of everything.. I am born to burn blood.. V.Born.. a cure a pure= a square B purest B curest= B square a square Bsqure proofs.. Sign-heart boy going=NON BoY.. I am null I am nothing I am never never never born again .. past and future.. I am present.. I am dies and I am rise.. rising sun..I am.. I am MAN..and the.. I AM REAL MAN... now.... PSYCHIATRIC BOB.B Bsqure proofs ###

I am give some calculation example..of PI 22/7 22+7=29 .......The moon one revolvin process in earth. 7×4=28 is calculation in human theory... but 1 is exists .. 7×3=21.......21+1=22 7 is 1 week 1=week 7=days 7+1 is 8 8 is (2+2)×2 2+2=4+1=5.. now the game times slovenian.. 22/7 (22+7)=2+2+7=11 ok..11=1+1=2 29=2and9 9 is higher of exists 3-6-9 2 is 1+1=11 11=one of one: 1 is null~1 is neutral. . the solo art is begin.... 22/7 divide 2 11/3.5 divide 2 5.5/1.75 divide 2 2.75/0.375 =2:75~375 2=7+5~3+7+5 2=27=27+2=29 but... 2:27 =2+2+7 =11 Bsquare proofs 22/7=11 thank you..

I am not talented.. I am simple boy..in anything.. I am give some example is PI MEDITATION(M)=11 that is 1=1 spiritual energy=1 holy heart is=1 so..1+1=11 this is TiMe artificial machine that is Time machine.. TIME full form=True inside mind energy.. that is convert T.I.M.E mind Feelings(MF)=11 brain parts is=1 Feeling imagine create=1 they are LiGht=1,speed=1 light speed =1+1=11 Time-LigHt-Speed=Artifical machine.. 11+11=22 ................... Lucky(L)=7 week of days=7 meditation energy create..7 wonder work.. but 8 WONDER WORK COMING SOON.. B.B-4Bsqaure proofs.. that is Bsqure times 2+2=5.. 0.25 .M.A.(N)... Making artificial arts nation Nest.. that is MAN...MAN was=1, that is=I I was man, man is only one who exists everywhere... B.B know everthing.. HE(S) is G.O.D.. great..originally...Development...Human-beings revolvin.. He's 11=1.1 Peri-lion Boy.. True spiritual truth trust..everything ok.. silent is best reason of make self development. . sound love you.. you find the reason of you want..and you aim ..dream... you are B.B=believe-beautiful= best brave works.. you are one who is exists.. you are 1-Trillions.. B.B......Bsquare proofs.. psychiatric Bob.b..0.25...

Lyagulyalyulin made boom 💥 in blogging

Well This kids doesn't know about Ramanujan 😎

NOT fair when comparing Newton's method with bisecting the polygons. The crux in Newton's method is that he's invented Calculus, which is not only a powerful tool but also a new branch of Mathematics.

I tried evaluating just one term, not performing any of the subtractions, and got 3.4. One digit was right, the leading 3. It looks like you get about one digit per term, very roughly. I can't believe how fast that converges. Just one subtraction term, and you're at 3.152 (vs. 3.1416). Wow!

The tombstone has an error at the 5th digit, this is kinda sad..

Great video. At 14:20, shouldn't it be x5/5 rather than x4/4 ?

Instead of inscribing polygons in circles, they should have tried dividing 22 by 7 :)

Ludolph Van Ceulen: “I spent 25 years to calculate pi with extreme precision” Isaac Newton: *S P E E D R U N*

3.14159265358979323846264338327

Why couldn't they just divide the circumference by diameter

Weird thing about Pi and reality: As far as modern physics goes, there is no meaning to lengths smaller than the Planck Length. It's not even theoretically possible to measure a smaller length. It's about 10^-35 meters. On the other end, it is not theoretically possible to observe sizes larger than the observable universe. That's about 10^26. This means 62 digits of pi are enough to calculate the circumference of the entire observable universe- the largest possible thing- to the precision of the smallest possible measurement. Digits of pi past the 62nd can never apply to an actual field measurement, not even theoretically. If, for some reason, the actual circumference of circles* differs from calculations at the 63rd digit or beyond, we would never be able to know. Those digits not only have no practical use, according to physics as we know it, they can't. *Possible in a curved universe!

You might laugh at the dude who spent 25 years of his life calculating Pi with an inefficient method, but he isn't the one wasting good pizza

This is poggers

My boy Kontorovich using a Greenscreen. Perhaps his sense of home is very private.

AMAZING

Amazing.

Errata @14:17 Third term on the bottom sequence should be x^5/5, not X^4/4, and last term should be x^9/9, not x^9/8. These corrections are consistent with the expression @15:58. I implemented this in Excel. After 17 terms it runs out of dynamic range (significance), but does computes π with full double precision. I sum the terms from the bottom up (Horner's rule), but the 18th term is: -7.41982E-16 and the sum of terms 29 through 18 is -1.13986E-14. In Excel 3.1415926535898000 -1.13986E-14 = 3.1415926535898000 and =PI() evaluates to 3.1415926535898000.

The crain and the brick analogy was simply a poor choise and bad

I wonder if pi is a dimensional constant; that is, for instance, in your dreams if you were to work out pi would it still be 3.141592.....?

14:19 why is x^9 divided by 8, shouldn't it be divided by 9 cause he said you multiply by x and divide by the new power, which is 9

Who else had their mind absolutely blown by the beginning pizza segment??

That's awesome even be ı'm enginnering..

Do Photons Have Mass? YES... I Sincerely Beg You To PROVE ME WRONG! ... and the Answer To The Universe Is -42 !!! The Mass of a Photon is Given by: m = (h/cλ) (kg) where, m = mass of a single photon c = speed of light, λ = wavelength of photon “Bozeon Constant” b is as follows: b = h/c (kg m) b =6.62607004x10^(-34) (kg m^2/s) / (299792458) (m/s) b = 2.210219x10^(-42) (kg m) The Mass of a Photon Is: m = b/λ (kg) or, m = 2.210219x10^(-42) / λ (kg) A typical Red photon with a wavelength of 700nm has the following mass: m = 2.210219x10^(-42) (kg m) / 7x10^(-7) (m) Mass of a 700 nm Red Photon: m = 3.1574557x10^(-36) (kg ) PROVE ME WRONG OR… Join The TTOE Team At BRAVE and Help Save Physics From Those With Warped Spacetime Minds: @BozeonResearchAndAEtherVerificationEtaireia Notes To Aid Understanding of what EM Dipoles Particles Are … The “Bozeon constant” “b” converts photon wavelength into the sum of all the masses of the “bozeons” or “God particles” that form the “quantum superfluid” in all particles. “Bozeon” is Polish for “God Particle”, the ethnicity of the Conceivor of EM Kinetic Dipole Theory, aka The Theory of Everything. There are trillions upon trillions of dipoles in a single photon. (more on the exact number later). Everything including all elementary particles are made of complex flows of EM Kinetic Dipoles. A Kinetic Dipole is a somewhat symmetric particle with one end that has more mass than the other. Bozeon’s are Electromagnetic Kinetic Dipole Particles that form the EM field. For better understanding you can pretend for now that the Planck Length is the RMS distance between kinetically colliding EM Dipoles (“Bozeons”). You can also pretend that the “size” of a EM Dipole is about 10^(-42) meters in length. The Dipole Mass Density Gradient in Vacuum determines the local force of gravity. Big “G” simply converts Dipole Mass Density Gradients into Acceleration. All forces EM, Gravity, Weak, Strong, are all calculated from the momentum transfers between kinetic collisions of these EM Dipole Particles. EM Dipoles in Vacuum are in a gaseous state and the “quantum superfluid” in all particles is liquefied EM Fields and are technically a Bose-Einstein Condensate of EM Kinetic Dipole Particles. Black holes are supersolids of EM Dipole Particles. Copyright 2021 John E. Boze

why dont people just divide the circumference with diameter?

We can find it, just use a rope and patch it up around a circle! Then the length of the rope is actually circumference! Another example is given in this video, just determine the length of pizza crust. Its the circumference

We don't know the circumference

The Way of Presentation of This Video and Visuals are Just As Amazing as content!!!!

Newton stole calculus from Leibniz

Which software do you use to make animation?

I am pretty sure newton was high 24/7...

U got me a little hungry

Do a video on ramanujan infinity series please ❤️❤️

6:45 sanskrit (india)

so anybody eating those pizza?

It’s not „on“ it’s OVER ie 1 over 3, not 1 ON 3

I don't understand it 😵

after learning differentiaition and integration, i finally understand it i love pure mathematics

In reality, there is no such thing as a circle. Only approximations to circles. That's because in the material world, any circle you make or is made, is made up of particles with finite size. They may be extremely small, but are still finite. even when speaking of electromagnetic fields, there are quantum nodes that are distinct entities. Thus all figures that look like circles are really polygons of n sides where n < infinity. That means the ratio of perimeter to radius is not fixed, but varies as n. The fact that pi is an irrational number should have been a clue from the beginning. Mathematics, in fact, is only a simplified model of reality. There are no infinitely small objects called points, or lines made up of these imaginary objects of zero size, etc. Our math is a very good approximation that of course has been extremely useful to us, but sometimes when we slip into thinking that it is absolutely precise, we can get into difficulties.

At 4:48 Did the poor mason who inscribed "1415926**3**35" instead of "1415926**5**35" have to refund any of the purchase price for that error?

I was just wondering, what happened to all those pizzas?

Excellent video! However, way more than a transformation of Pi... great explanation of Newton's expansion / insight into the binomial theorem and Pascal's triangle =)

That's why ,we say smart work is better than hard work !

*People talk about Newton cause he labelled hisname on science, but no one talks about Bhaskaracharya, because he worshipped science...*

This is magical

Each and every one of us deserves a pizza for watching this

pineapple pizza is great. fight me.

Mind blown!

Pizza's just gone cold.

At 23 I was just trying to work out a formula to pay my student debt...

How do you know how many decimal places it is correct to if that’s the best algorithm it came out during that time? Does that mean there was another algorithm that’s even better?

@MuffinsAPlenty thank you so much for your explanation. I understand now

For the Archimedean method (polygons inside and outside of the circle), well... Archimedes didn't have decimal notation, so he didn't use decimal places. (Decimal notation as we know it today didn't really exist until the 16th century CE.) However, if you were to try to do it, you would do it like this: the polygon _inside_ the circle has a smaller perimeter than the circle, and the polygon _outside_ the circle has a larger perimeter than the circle. Therefore, you get an upper bound and a lower bound for pi. If both your upper bound and lower bound agree to 3 decimal places, for instance, then you know pi must have those same 3 decimal places. Now, for Newton's technique, that's a little bit trickier! What it essentially boils down to is checking how big later terms in the series are and understanding that the series "converges". If the later terms could only add up to give you a value of, say, 0.00002, then you know your approximation is correct up to 3 decimal places. If you want to learn more about this technique, you can look up the "Alternating Series Estimation Theorem" which is one test for a certain type of series. But there are other estimation theorems for different types of series.

I found a way to calculate value of pi with increasing precision. The formula is Pi = Lim{(n/2).sin(360/n)} as n -> infinity. For variety, I have another formula:- Pi = Lim{n.sin(180/n)} as n -> infinity. Both these formulae don't give same results for a specific value of but they give values closer to the Pi given by calculators if you keep increasing the value of n.

@Релёкс84 Still, we can use a calculator 😋. Even though most calculors give the value of pi but using a formula to find it is more satisfying.

But then you run into the problem of calculating sin with precision. It's very easy to calculate powers of x, but sin(x) is much harder.

Archimedes

Great video...Love from India

Pi's round, cornbread's square..

Newton

now they discovered that math is racist... how about that

@nothing to see here move along loll just look it up lol

lol what