# Why is pi here? And why is it squared? A geometric answer to the Basel problem

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- Published on Mar 2, 2018
- A most beautiful proof of the Basel problem, using light.

Home page: www.3blue1brown.com/

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

And by Brilliant: brilliant.org/3b1b

Brilliant's principles list that I referenced:

brilliant.org/principles/

Get early access and more through Patreon:

www.patreon.com/3blue1brown

The content here was based on a paper by Johan Wästlund

www.math.chalmers.se/~wastlund/Cosmic.pdf

Check out Mathologer's video on the many cousins of the Pythagorean theorem:

usclip.net/video/p-0SOWbzUYI/video.html

On the topic of Mathologer, he also has a nice video about the Basel problem:

usclip.net/video/yPl64xi_ZZA/video.html

A simple Geogebra to play around with the Inverse Pythagorean Theorem argument shown here.

ggbm.at/yPExUf7b

Some of you may be concerned about the final step here where we said the circle approaches a line. What about all the lighthouses on the far end? Well, a more careful calculation will show that the contributions from those lights become more negligible. In fact, the contributions from almost all lights become negligible. For the ambitious among you, see this paper for full details.

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.

Music by Vincent Rubinetti:

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

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Kirk Hodges15 hours agoDude, don't show tau in your visual for pi (1:30) and think tauist won't go nuts.

Hoiman Siu16 hours agoHoly moly thats so creative

Lochlan SmithDay ago11:31 he almost summoned satan for a moment there.

karolak kolo4 days agoMy favorite 3blue1brown video!

I'm rewatching it for the 4th time!

Sondre Grøneng4 days agoNow, it might be important to note for anyone considering building an infinitely large circular lake with evenly spaced, perfectly identical, light houses, that this would only work in a vacuum with no light pollution.

ccdsah4 days agoSo much easier with calculus

Imran Shishir7 days ago^{+1}And my brain just shattered into a infinite number of pieces.

Sherin Funmes7 days ago^{+43}*Pi is like an uninvited guest who shows up at every party where he isn't supposed to be*

surfer8554 days agoEven Mister Bean hates Pi, for showing up at every party he goes with his teddy bear!

Riccardo Foschi8 days agoTha quality of your videos is remarkable! You make hard math problem easy even for me that I do not have a mathematical background! Thanks for your great work!

Yo wut9 days agoWhat. I googled 'basel pie'

Carlos Yuichi9 days ago^{+1}3blue1brow:YOU GET A PI, YOU GET A PI TOO, *E V E R Y O N E* GET A PI

Muhammed Ali10 days agoEveryone animation..blowing my mind

Claylo10 days ago^{+1}6:02 On the left? That seems to be right...

Дима М-Преображенский11 days agoFckng great!

DavidGP11 days ago^{+2}Mindblowing stuff, presented by the most soothing voice imaginable. Awesome

marwan aljohary12 days ago^{+3}That was the most exciting math lesson I've ever been to.

Thank you for making math so fun.

j s12 days agoSo confusing

Dark Knight12 days agowhat software is he using to visualise this?

Federico Masini13 days agoThis is so awesome!

Alex Homer13 days agosomeone do some math on my symbol... : )( : triangulating circles with squares, haha

Alex Homer13 days agoalways wondered why I had an affinity for St. BASILS cathedral

Toni Scott14 days agotry explaining in the beginning.... unless you don't want ppl to know why the light is 1/4 more...if you are smart you can explain the why...

Tilo Droid14 days agoI don't get the "multiply by 3/4ths" thing

bazoo51316 days ago^{+1}Risking to be accused of using a pun, this is brilliant!

Isheta Bhatt15 days ago^{+2}You iridescent moonbeam!

Loveena Saran19 days agoHow is that the apparent brightness on that point is 1/d^2 for the circle ??🤔

Ornithocowian King20 days agoDear Ben: amazing video my dude

gk1000200020 days agoIt is always interesting to see how some underlying things have a physical basis

S0L4ZUL21 day agoCan you find relationships of these rectangles mentioned in the video (in link below) to circle(s)?

usclip.net/video/8t1kkXYb8Ro/video.html

Pratik Joshi21 day agoCan you please explain why the sum of all the natural numbers is -1/12 as per Ramanujan?

Jai Carlson22 days ago^{+5}that settles it. mathematicians are witches, and must be burned at the stake.

Kenneth Garringer22 days agoVexed causes cancerous

Kenneth Garringer22 days agoGuide lines taxes

Kenneth Garringer22 days agoLasers

Kenneth Garringer22 days agoYou're right cost money

Kenneth Garringer22 days agoTrue

Kenneth Garringer22 days agoGround ing

Kenneth Garringer22 days agoEngery

Kenneth Garringer22 days agoAnd cutting down a lot of Forrest s

Kenneth Garringer22 days agoInterface

Kenneth Garringer22 days agoIn our township mean s higher engery bills.

gerardo santana trujillo23 days agoVery nice, thanks a lot!

PASUNURU SAI VINEETH25 days ago0:53 As a Fedfan, I am so proud that Euler is also from Basel 😇

Sabertooth Turtle28 days agoAm I the only one who noticed at 0:53, that the physicist who posed the mathematical problem did so in year 1644 and the answer to his problem was discovered almost a hundred years later, the answer was 1.644. Spooky.

葉修誠29 days ago太神奇了

Lim Pro29 days ago^{+1}amazing

Deyu ZhangMonth agoThank you! Your class is also so hot in china! Can you open a pay way in China we want to support you

surfer855Month agoVery good!

Abhishek VankitMonth ago^{+1}So there's good reason why everyone is not great at math

anelepercon YT jr.Month ago^{+1}0:45 Answer: *1.644* 984... Proposed in *1644*

james vanMonth agoAlthough I didn't understand it, I still want to praise it.

Gwebanget ForeverMonth agoA=Pi.r^2 is okay. But C doesn't equals 2Pi. To prove it, please examine 15° or below, on triangle's base line [ 2sin(X/2) ], arc line [ (X/360)× 2Pi ] and 'neck' [ (1-cos (X/2) ].

David TerrMonth ago^{+1}Wow, this was a very enlightening derivation of Euler's formula! (pardon the pun!) I never imagined this formula was so closely related to circular geometry. I wonder if it's possible to devise similar geometric proofs to the formulas for zeta(2n) in general.

gk1000200020 days agoUnfortunately the complex number domain used in such things and in Fourier Series and stuff becomes a stretch in the real physical world

Dustin GunnellsMonth ago^{+1}You are Appreciated!

Fenil KamdarMonth ago^{+6}After every amination

Me: Wowww!!!

Konstantin KouptsovMonth ago^{+1}I cannot say I am convinced.

zhang东Month ago14：32，从这里开始不懂，为什么负数会参与进来，为什么分母都是奇数

xx ab action xxMonth ago^{+1}???, shouldn't the radius be 0.5 at 1:31

jhony angaritaMonth agoLo único que hay que entender es que curva o recta es la forma de la línea

Una línea curva no es una línea recta ni está compuesta por rectas el

Concepto de pi está mal enfocado

Procedimientos como algoritmo están elaborados para hallar los lados de polígonos

Una circunferencia es una curva cerrada

Uni QuEMonth agoCan you spot the mistake?

usclip.net/video/-427CFwZcEM/video.html

Aaron FarishMonth agoOk I get it

Ivan ZrinskiMonth ago^{+1}Best Teacher ever!