# Pi hiding in prime regularities

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**Published on May 19, 2017**- A story of pi, prime numbers, and complex numbers, and how number theory braids them together.

Brought to you by you: 3b1b.co/leibniz-thanks

Home page: www.3blue1brown.com/

And by Remix: www.remix.com/

The fact that only primes that are one above a multiple of four can be expressed as the sum of two squares is known as "Fermat's theorem on sums of two squares": goo.gl/EdhaN2

Music by Vince Rubinetti:

vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

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Sarthak GirdharHour agoWait. Is this content for free? Are you kidding me?

Galileosays10 hours agoIncredible. How many cubic lattice points in a sphere?

풋볼리딩Day ago한국어 번역해주신 분 감사합니다.

*Zls one*3 days ago26:35 can you see binery?

markovic693 days agothank you mate, just thank you .

Vrajesh Vyas3 days agoThis was discovered by Madhava

usclip.net/video/B8IB6D6Ew_8/video.html

usclip.net/video/nU4ekwkXHYw/video.html

As if that was not enough he coded it in a verse with following strictly the meter. Great Combo of Right and Left brain

Shahar S.3 days agoYour proof is fabulous, BUT…

You ignore a very important part:

You say that the number of lattice points on √N circle is 4(x(1)+x(p1)+…)(x(1)+x(p2)+…)∙∙∙

How can you prove that all these points are distinct ? If you don’t prove it, the number of points may be smaller.

왕고구마4 days agoAt last 3B1B is beginning to touch the deepest secret of the universe.

Sheldon Wu4 days agoOh my god. I watched from the beginning to the end.

The Masked Man4 days agoWhat the fuck is χ?

Ni Lin5 days agoI don't know if you have the same experience: Whenever a math teacher explains to me a math theory, at some point I'll encounter something that the teacher deems trivia. But it's impossible for me to keep going without fully understanding this 'trivial' matter. Is math teaching really just a teacher with arms teaching a roomful of students who may or may not have arms how to arm wrestle?

Quwertyn5 days ago4:35 can someone tell me what he's saying?

Naté Slough6 days agoΧ(n) = sin(n * π / 2)

DEWILL6 days ago^{+1}Seriously, we don't deserve this quality of explanation. And we cannot express how grateful these videos are.

You deserve my loudest clap ever. Thank you.

physics crush6 days agoIs lattice point can be of any dimension?

débora tayná8 days ago^{+1}Please, someone who speak english and portuguese fluent translate the subtitles of this video for portuguese. Pleasee

Diego FCM4 days agodébora tayná

Coloca em espanhol se vc tem dificuldade com ingles

ilprediletto9 days agoWOW!!!!!

Thumbomb9 days ago1:46 "Who am I really?"

XDDD

Mats Leandersson10 days agoThe best explanation I’ve ever received (to anything I’ve ever wanted to know). 👏🏻👏🏻👏🏻

Harambe McHarambeface11 days agoOk, that is super cool

Sylwester Bogusiak12 days agoPrimes are Fibonacci dependants.... in a halfway ;)

Look this...

New formula for prime numbers? ... something about density of primes in 2D space...

SP=1/2*Phi

SP= (((P1+P2+...+Pn)) / QP)/GF

Where:

SF < Pn

Sylwester Bogusiak12 days agoPrimes are Fibonacci dependants.... in a halfway ;)

Look this...

New formula for prime numbers? ... something about density of primes in 2D space...

SP=1/2*Phi

SP= (((P1+P2+...+Pn)) / QP)/GF

Where:

SF < Pn

Aryan Mishra13 days ago^{+1}My friend asked me that what's this 3b1b channel and i told him that its the π lovers channel

Jinil Kaiser14 days ago와.....

LOL Science14 days ago^{+1}Wow I actually understood it from the first time...

Give me a Nobel prize!

Thái Sơn Lương15 days agoWho came here for studying English? 😉😉😉

로직 LogiQ16 days agoI’m korean middle school student. I’m really surprised by your unique and amazing idea. I wonder what your job is. I really enjoy your videos. Thank you for making these videos.

Emmanuel R.18 days agoHEy 1:10 he made the illusion of black dots of intersections, black dots only appear when you see them.

R. Mo19 days agoI'm a "spreadsheetdologist". I love writing functions and using large lists of numbers as inputs to see what happens. I guess I'm some sortof number tinkerer. I'm sure that I have discovered a few things in number theory using my unconventional ways of messing about with spreadsheets, but at 53 I'm a bit old and hessitant at revealing how I probably re-discovered things others already know and can describe in a mathematical way (which I am trying to get to grips with using my limited knowledge of the subject). I'm using spreadsheets as an anvil to hammer out and see what comes out. hahahaha. Love this video and others made by a talented guy and his team. Thanks and keep it up.

kuba feder21 day agotruly amazing, thank you for explaining beaty of math to ordinary people like me, u are doing it great

Hakan Çakıcı22 days ago^{+1}Yep, it's big brain time.

Attornado Andrea24 days ago1 is not prime. 😭

Aayush Patel24 days agomy brain hurts😓😓

Skittus25 days ago2:56 3,6 roentgen. Not great, not terrible.

Ashley Stone29 days ago:O damn we should be taught this form of math from a very young age. Imagine having an intuitive grasp of 2-dimensional numbers the same way one has of a number line.

nikki.creeps around.on.holidays29 days agoSoooo.... Who also thinks quantum physics is easier?

wwwjeafcomMonth agoSo, Pi, after all, is cousins with Prime. Both are a Circle, a Big Ban, based on 12. The Squaring of the Circle is how Pi came about. It has numbers based on 60, which is an ancient Sumerian base number. Easy to Square the Circle. Which means, the Ancients, before the Event 12 thousand years ago knew about the Squaring of the Circle as well as our best mathematicians. They should investigate the ancient structures and documents in order to acquire knowledge from the ancients. I believe those ancient stones were left for us a Time capsule dealing with an event that will occur in their future. They knew they would be wiped out, so they must have had a way to shelter from the “storm,” that would engulf the Earth 12,000 years ago.

We need matemática to understand the cycle of Betelgeuse, the next event. That star with a cross piercing its fury. An orange supergiant about to collapse and we are in one of its dipoles, too close for comfort.

We need to understand the cicles that rule the universe, perfectly tuned to the 12 notes of music.

Are the 12 notes cousins of Pi and Prime.

It all makes perfect sense.

Thanks for your math

Eduardo AlvearMonth agoPi is Prime’s cousin. They have the same father, a circle. Which comes out of 12 and 16, and goes on. Ancient knowledge it seems to me you have tapped into. I see the force is strong with you. Thank you! I can finally say the Pi is a prime number intimately related since the Big Bang, in a circle, a two dimensional expression of a three and fourth dimensional expression.

Thanks, you are very inspiring. Thanks for sharing your brightness. :)

gideon yuvalMonth ago3B1B - your math videos are so good, I'm wondering if you have a twin brother (or sister) who covers other topics, such as physics?

Feras HamdanMonth agoSuper nice video

ObscuritéMonth agoThe way he places the shameless self promotion is funny

Frazer KirkmanMonth agoThat was done of the most beautiful math I've seen, and so well presented. Thank you so much.

EricMonth agothe greatest video i have ever watched,thanks!

slayer 1Month agoAlthough this is a very good video excellent editing and thought-provoking I would like to see an application show the actual math say like building a bridge or launching a rocket or my most popular thought would be auto mechanics it has electro-mechanics Hydro mechanics thermal mechanics kinetics a world of different math that I have never really used but would like to know about I've been a lot of mechanics would like to know about things like that also not only mechanics engineers in general

문수혁Month agoHow incredebile

Smogy 001Month ago8:16 "this might seem needlessly complex"

I see what you did there

TheFamousArthurMonth ago83 and 89 are sexy primes.

TheFamousArthurMonth ago89 and 97 are octopus primes.

TARUN AKASHMonth agoat 9:09, i figured where it is going.

INDEED of LIFE'SMonth agoi am u r big fan sir

...thanks for everything 😊😇

GreatFlamin ZeusMonth agoCaption Error: 9:58-10:01

You say “[multiply by i & -i]” but the caption says i & -1

Also the captions can’t handle superscripts or the like so exponents look like coefficients.

Santiago PachiarottiMonth agoExcelent video! Congratulations

Imagine ExistanceMonth agoMy favorite pi formula is

x=1

x=x+sin(x)+sin(x+sin(x))+...

Or a loop of

x=x+sin(x)

it adds the error of the distance from the nearest whole multiple of pi

if it is below a multiple it adds the sin getting closer to pi

If the multiple ahead is even, it goes to the previous odd one and if ahead of a odd one it goes forward

Nicholaus UhlMonth agoThere was an optical illusion at ~7:55 where all the dots, besides the ones you were looking at directly, were hollow.

Luke JohnstonMonth ago25:00 probably the most ridiculously excessive and beautiful way to find the factors of a integer.

David VicenteMonth agoThank you for your video!

Is your video inspired by "Geometry and the Imagination" written by Hilbert and Cohn-Vossen?

LeifMonth agoYou said 3.is a multiple of 4 at 11:07 in the video? Mistake..not on purpose unlike the Martin Sheen comment I'm assuming...neither is 7 for that matter..

LeBGDU17 PkTuDorPaMonth agoThis is the single most crazy math video I have ever seen in my life. Your videos are of a rare quality. To say the least. Wow. I'm just... just literraly speechless. You are, like maths, incredible. Huge respects.

David WilkieMonth agoWhenever information is arranged in a crystal type resonance arrangement, ie has a state of "two-ness" and the probability effect that's noticed dropping pins or nails on the parallel lines grid, it's a situation that shows up as Pi, a specific "calculation" that demonstrates a similar consequence in the above example.

As an interested Observer rather than a practical Scientist/Mathematician, ..watching presentations like these reveals much about the mechanism of the Universal interference connection, e-Pi-i, that I cannot put in intelligible words. (That's why these videos are so very impressive)

Kutluhan Bilgeşah BayzanMonth agoX(n)=cos(πn/2)

THE POWERFUL2 months ago^{+1}If you add quaternions...

so ia2 months agoHablen español pesados de poronga

Jaime A Farah2 months agoBeautiful video !

it seems all roads lead to π

드라불리2 months agoThis vidios support korean... but still I can understand

⬆stupid⬆

서명교2 months agoWait a minute... doesn't your last part needs more explanation? There are R^2 terms on left side so we can't be approximate the sum like that isn't it?

Michael Lubin2 months agoThat was awesome. Thanks! More algebra than most of your videos, which is probably why I understand it...

Alessandro Tagliafierro2 months ago^{+1}My words can't possibly express the amount of respect and admiration I have for you after watching this kind of videos

zehao zhao2 months agowhat number theory book are you using?

Kelsey Phillip Payne2 months agoOne of my favorite math vids of all time :)

Jasper Kole2 months ago"Factors of 2 just don't make a difference"

*Mercene primes cry in the corner*