Approximating Pi ( Monte Carlo integration ) | animation

Pi approximation using Monte Carlo integration.
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Support my animations on:
/ think_twice
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Any further questions or ideas:
Email - [e-mail]
Twitter - / thinktwice2580
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Programs used:
- Cinema 4D
- Processing
- Adobe Premiere Pro
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[@abaybektursun]

Love from from 3Blue1Brown

[@themaverick1891]

You are not 3Blue1Brown.

[@joshuaabraham7308]

@@themaverick1891 Or is he...? Michael Vsauce here

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@@joshuaabraham7308 No, he is not. You aren't Vsauce either.

[@herobrine1847]

@@themaverick1891 I’m not 3Blue1Brown I’m unhappy

[@tapksa]

A lot of people seem to be asking why would someone use this somewhat inefficient method to approximate pi. I'd say this is more an illustration of using randomness as a basis for a simulation, pi is just a simple and visual example.

[@AnantTripathi1by0]

this channel deserves atleast a million subscribers. It really makes me sad that this channel isnt getting all the support thnx 3b1b for bringing me here.

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[@Technomancr]

Came from 3b1b, stayed for the awesome content.

[@mlsgames938]

your videos are juste amazing you give us a new understanding of the thing, you are really doing a great job, kisses from France

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Amazing, loved it!

[@ThinkTwiceLtu]

Nuno Mateus thanks man:)

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How on earth can you think that awesome think. GENIUS

[@Anonymous-8080]

True

[@jsaavy]

I use your videos to show my students the beauty of mathematics and to drive home concepts with these amazing visual aesthetics. Thank you!

[@sam2026]

definitely a novel way to compute pi that children could understand. Your video is a great and has use in teaching.

[@facitenonvictimarum174]

Aleph Naught ...OK then play that video AS IS to a bunch of children and see how many understand. Thanks... (they'd love Who's on First though)

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I'm only two videos in but i really feel you deserve more subscribers. Great work

[@porfavorrecuerdameestudiar7071]

Cool. Great work!

[@xjonnyd93x]

Your visualizations are outstanding! The music also adds just so much to it!

[@ThinkTwiceLtu]

thank you~

[@DanaTheLateBloomingFruitLoop]

This is really cool.The youtuber alphaphoenix did this as a practical experiment with raindrops and got pretty close

[@PiErDzoncy7]

Great job and thank you!

[@osbyrne]

so incredibly cool yet so logic

[@cavver3523]

Please keep doing these videos. I love your videos as much as I love maths! THANKS!

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3b1b brought me here

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Cool..

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Yep. Me too. Liked and subbed....

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Damn. Burned through all of them way too fast.

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The best explanation in short time

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You deserve more subscribers. Great video as usual.

[@ThinkTwiceLtu]

Gurpreet Singh Kakar thanks a lot

[@vithei477]

Great channel, keep up the great work! I am so happy 3b1b brought me here.

[@balajisriram6363]

that probability trick made me laugh. that was brilliant!!

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Awesome!!

[@briann363]

Cool video as always

[@ThinkTwiceLtu]

brian nguyen thank you!

[@user-pi1rn9hd6k]

I love this chanel. As an ex-math teacher I think any math teacher must use this videos in his classroom on a big screen. A great way to make ABSTRACT issue into VISUAL. (Sorry for bad english) I wish I had this chanel when I teached math. Maybe it will help to add vocal explain. Anyway ty 4 beautiful videos!! Tamir Erez. Israel

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so satisfying

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This is just beautiful. 3b1b sent me here and I'm glad

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Sir u rock

[@AlexSFM]

I got this on my recomendation feed somehow and I didn't thought I would enjoy a math lesson like this

[@ml-simplified]

Amazing!!! Love from 3Blue1Brown fan

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3Blue1Brown brought me here. Amazing videos! keep it up!!!

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Amazing vídeo.

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Great

[@debajyotimajumder472]

**bows** neat sir, very neat !

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Came from 3Blue1Brown. Subcribed for more amazing content :)

[@DanielSantos-ct6vr]

Cool

[@RomanNumural9]

Beautiful! A video on fixed point iteration might make for some cool visuals

[@ThinkTwiceLtu]

thanks:) I will keep that in mind

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i hope people interest with this channel... your content is really good and cool.

[@ThinkTwiceLtu]

[Alfraganus] thank you very much

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Wow, this is awesome and easily comprehensible. Thanks to 3blue1brown I've discovered you and I'll subscribe to your channel

[@ThinkTwiceLtu]

Thanks a lot for the support!

[@aymenzaki6786]

very nice animation thnx

[@ThinkTwiceLtu]

thanks!

[@-Mike-]

I never understood why it has to be randomly generated points to approximate pi. Isn't it easier to put the points homogenously on the square?

[@ASLUHLUHCE]

Watch this channel blow up (currently 26k subs)

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Great stuff, we need more youtube channels like this! Subscribed

[@jerryhu9005]

It doesn't seem to converge very quickly though...I mean, if you were looking to go to say, 10 digits of accuracy, how many random points would you need?

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Here before 1 mil subscriber xD

[@user-qs4lc2we5t]

This and 3Blue1Brown is great

[@snowyshade0901]

Fabulous... Now I can't concentrate to my maths teacher cuz he doesn't explain clearly as you do ;_;

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You should seriously consider maths hentai as a career path

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Porn plot be like "Come here girl so i can square root your pie!"

[@jsmcguireIII]

Wouldn't the Central Limit Theorem require >30 random points?

[@fawadmirza.]

I saw this approacc on the coating train :D

[@snowman7514]

PInteresting

[@lithostheory]

Nicely inefficient!

[@yyytis2069]

I made this 2 years ago. Cool

[@alvkarthik2018]

so those point and accounting for the area of the circle and square.. more the points better the approximation

[@namannarang4208]

I really had a question I have seen many of your animation proofs but do you plan to like present non animation proofs in the future

[@ThinkTwiceLtu]

batman rules maybe, but probably not in a near future

[@neslef3]

Very interesting. What was your method for creating the circle without using pi in the first place? Do you just create a center point and then use the length of the radius to determine whether a given point is within the circumference or do you use another technique?

[@ThinkTwiceLtu]

neslef3 yes I checked if the distance from the center to the point is less than the radius of the circle

[@ovebepari6682]

Dayyyymn.

[@lorincszabo7411]

this is the video i show to everyone when asked about monte carlo :) so simple so visual :D (the other one i use is "wisdom of the crowd" about counting jellybeans and the german tank problem :D statistics and random at its best serving entire mankind :) )

[@jkoh93]

how does it know if the random point is inside the circle? visually or distance from circle < r? can you also use this to integrate random squiggles not defined by nice formulae? then that would need to be done visually. wait, isnt that what we all did in primary school trying to find the area of a random shape? except instead of random points it was going through all the squares it intersects with

[@joeyhardin5903]

Before I even came here, I made a code just like this on scratch. I left it on for 14 hours to plot 1,000,000 points and the result was like 3.245 😥 It also wrecked my computer

[@ThinkTwiceLtu]

feels bad

[@gaelbizet4438]

And we can add that he used a shotgun (He shot on a target inside a square) to make his first approximation! True story :)

[@rlstnnl1740]

What music did you use during this video?

[@blu5037]

Damn

[@notsoclearsky]

Btw didn't the computer display the circle using the value of pi fed to it in the first place? Anyway great content. Really boosts my interest in maths.

[@tapksa]

Probably in the visualization. But as for the actual computation, you can just check whether your random point is within the distance r from the centre of the square. You see?

[@rikjandijkstra205]

What if there are 5 dots inside the circle and 5 outside the circle. Then you would have 4*(5/5)=4

[@sm-zt4ut]

Is the code allowed to choose the same point twice? Would allowing it to do so have an impact on the results?

[@matthewreese7710]

I doubt it would have an impact as what we are really looking at is the chance any random point will be in the circle or not. The chance it lands in the circle or not is the same whether or not some other point has landed there before.

[@ohboy1113]

Yo I feel like a genius I thought of this while looking at a pizza.

[@AffeAffelinTV]

so how do you describe the areas of the circle and the square? the square in x and y coordinate and the circle with ✓(x²+y²)≤1?

[@jaromir.adamec]

The way you sugest, only take square of both sides of the equation. Specifically, for given x, y ∈ [-1 , 1], test whether x·x+y·y ≤ 1

[@ThePharphis]

IS the error reduction logarithmic? Square-root?

[@naukowywariat7123]

"Monte Carlo" method by Stanisław Ulam

[@nonexistence5135]

Was expecting something a bit more clever than plotting random points tbh

[@memyselfandtau4712]

How dare you approximate my value??!??

[@themaverick1891]

Because I can and I will.

[@irvinghernandezledezma4400]

You can compile in c++, specifically you should do it in linux with g++ compiler if you use windows you will have to change headers files only you put extension .h #include #include #include #include using namespace std; int main() { int c, at; double x, y, sumac, pi, r, ac; srand(time(NULL)); cout at; sumac=0.0; for(c = 1; c

[@kundanborakb]

Came from 3b1b :)

[@hymanimy]

You can do the same thing with throwing darts at a board ;)

[@ThinkTwiceLtu]

true:)

[@ThinkTwiceLtu]

you can also draw the square and a circle on a piece of paper and then leave it in the rain for a minute or so

[@reactandgame6894]

**cough** physics girl **cough** kzbin.info/www/bejne/g2SXhYJtZrh-fc0 **cough**

[@albertrenshaw4252]

How do you determine if a point is within the circle or not though, unless you already know pi?

[@erylkenner8045]

Albert Renshaw By finding the distance to the center of the circle. With R^2 >= x^2 + y^2. So given the (x,y) coordinate of a point, as well as the circle's radius R, you can check if that condition holds.

[@albertrenshaw4252]

Eryl Kenner ahh thank you! So obvious haha, I need to think more before I speak

[@yashasvprajapati6851]

What was the code, could you please share?

[@rajasharan86]

Inspired by this video I created this simple demo: rajasharan.github.io/simple-monte-carlo/

[@yoavboaz1078]

How do you even thinking about it

[@Galva94a]

Man, was that convergence slow...

[@bhavyajainnd]

Wow and how did the one who found this did it? I'm sure he didn't know coding back then

[@burthpinmc5489]

Bhavya Jain You don't need the coding You can prove the probabilistic inequality and squeeze it by infinity. (stochastic method) Wonderful mathematics.

[@bhavyajainnd]

Sury Bury wow that sounds interesting 😀

[@trobin]

hello, everyone coming from 3b1b’s channel, feast your eyes!

[@tupleee]

Monte Dé Carlo

[@fahadahmed8172]

It might be elementry question but why cant 4(2r) instead of 4r^2 in square Please can anyone elaborate.

[@fahadahmed8172]

@think twice

[@matthewreese7710]

2r is equal to one side length of the square. (2r)^2 is 4r^2, which both give the area. 2r times 4 is the perimeter, as the share has 4 sides all equal to 2r.

[@penatoliy]

Mote Carlo is king of smart random) But its never get true value, cuz Pi cant be represented as fraction.

[@GERhashim]

How do you know if the point is in the circle ? You need to draw a circle. How do you draw the circle ? You will need Pi. So you are using Pi to calculate Pi That does mean you will not get better accurate Approximation of Pi than your original Pi that you used to draw the circle. So what is the point?

[@netsouba5124]

Ger hashim A point is in the circle if its distance with the center is inferior to r so you don't need pi

[@GERhashim]

oooh now i got it. thank you got explaining :)

[@cristiantomi2188]

Now i like maths

[@That_One_Guy...]

Huh this is the same trick that Joma showed 🧐