A Random Way to Calculate Pi

Happy Pi Day!
Animated with:
The Manim Community Developers. (2021). Manim - Mathematical Animation Framework (Version v0.12.0) [Computer software]. www.manim.community/

[@nubdotdev]

A number of people have asked to see the code for this approximation, so here's an implementation in Python: from random import random total = 3141 count = 0 for i in range(total): x = random() y = random() if x*x + y*y

[@piedepew]

You from which university bro?

[@mainios126bobeats4]

A one liner I made (with some code to print the result nicely): from random import random from math import pi total = 1000000 def approximate_pi(total): return 4 * sum(random() ** 2 + random() ** 2

[@__lasevix_]

@@mainios126bobeats4 you should implement the function as a lambda

[@mainios126bobeats4]

@@__lasevix_ When I said one-liner I wasn’t referring to the whole approximate_pi, I meant the code inside. But here: from random import random approximate_pi = lambda total: 4 * sum(random() ** 2 + random() ** 2

[@aronbucca6777]

By the fundamental theorem of engineering pi is equal to three, it's simple

[@natedor7739]

i am completely amazed at the fact that this is not extremely popular considering how clean this editing and explanation is

[@nubdotdev]

Thanks a lot!

[@quintium1]

@@jay1373 Not the method, but the video

[@dfsgjlgsdklgjnmsidrg]

thats because there is no way without a quantum computer to generate true random numbers, therefore this experiment is always biased

[@direwolf27]

Newton did it better with calculus and Pascal's triangle

[@LymiaKanokawa]

@@dfsgjlgsdklgjnmsidrg Most modern CPUs contain a hardware RNG that uses quantum mechanical effects to generate the raw randomness. This is demonstrably false, and a lot of our current internet security relies on the fact that this is demonstrably false.

[@joebykaeby]

“A bit over 3,000,” you say. That wouldn’t be 3,141 by chance?

[@lyrimetacurl0]

4000 would have been better since then the result should be ~ 3142/4000 (it rounds up)

[@rupert_1491]

You actually counted it

[@flotzle3685]

@@rupert_1491 No, that's what pi is lol

[@silenceisgolden1758]

0:44 top left shows it

[@almostperfectbruh3517]

bro did you just count all of them

[@rjms06]

"A bit over 3000" I see what you've done here

[@nubdotdev]

;)

[@johnchristian7788]

Can someone please explain the joke?

[@realmarce]

@@johnchristian7788 Pi is a bit over 3 Its not that hard to understand

[@maiq_6821]

@@realmarce your reason for lacking bitches is also not hard to understand

[@vari1535]

@@johnchristian7788 They used 3141 points, which is the integer part of 1000π

[@abdullahaddous7081]

That's great. One thing I find interesting is how points are meant to be dimension less, yet we use them to approximate area.

[@pigmounterboardriver2839]

It's not area it's a ratio

[@xGOKOPx]

@@pigmounterboardriver2839 Yes, ratio of areas.

[@milaanvigraham8664]

That's kind of like saying dy/dx has two dimensionless entities (both numerator and denominator) but we use it to know the rate of change/slope of a real quantity. Interesting thought you brought up, but it's quite intuitive. It's not the dimensions of the point that matters - it's the probability that it will lie within the area vs out - the point's dimensions don't matter, but these areas'

[@MattMcIrvin]

It's interesting to think about. The points are dimensionless, but the probability density has "per unit area" units, and that's where the area comes in.

[@QwertierMannier-yp2hb]

Infinite points make lines, infinite lines make area. Limiting to infinite points approximated area

[@mrK29011]

I may be a lil bit of a geek. But I still do this from time to time just for fun. Especially on Pi day even though I am a medical student now my passion for mathematics has never faded😂. Subscribed🙂🙂🙂

[@vishwarao6064]

Woah its the opposite for me

[@primenumberbuster404]

This is basic Monte carlo sampling.

[@primenumberbuster404]

@@coreyhollaway7368 Math is suppose to be hard and nothing to feel embarassed. It keeps getting hard as you climb the ladder. Just give enough time. Also, I don't always recommend self study for Math because in most cases you get to miss a lot of interesting problem solving techniques, intuition and proper mindset. This could be avoided if you get yourself a very good mentor. Think this like a olympic mental sport. That's why Math Olympiad coaches exist.

[@panzerkampfwagentigerausfb6378]

You did a great job Justin! It's always cool to learn something random here and there, I already can see myself telling this to a random friend at a party lmao.

[@playify5538]

POV: you were trying to find some anime videos but you get this in your Recommended

[@pafnutiytheartist]

We actually coded this for CS class a few years back. Good times

[@drenz1523]

How is this channel and the video not that popular already?

[@revenevan11]

Just found your channel and subscribed, I hope you keep making stuff like this from time to time!

[@yuma9325]

commenting for the algorithm, this is some amazing stuff!

[@frankineskinecense]

This is how schools should teach maths. They have to visualize it and explain how a certain formula is made.

[@randomguyeverywhere6535]

Props to those people who actually counted the dots.

[@clashoclan3371]

The computers counts it.

[@janni4541]

It would be also very interesting to see this method compared to a method using evenly spaced dots and comparing them! This would also raise the question at what number of points one is more exact than the other.

[@FM1234]

This was actually a challenge to approximate pi in python during my first year first semester class on programming

[@thecandybarbandit6887]

Imagine losing count of your dots

[@corbi06]

you can also get rid of a random: count = 0 rad = 1000 total = (rad*2)**2 for x in range(rad*2): for y in range(rad*2): if (x-rad)**2 + (y-rad)**2

[@garrettrhoads6329]

I saw this and thought “huh, I could code that…” and then I did… it’s been four hours

[@kienthanhle6230]

you sucks at implementation then lol

[@mhmd-mc113]

If you want help, I'll gladly do

[@garrettrhoads6329]

Nah thx tho I managed to make it with turtle and a pure math one that’s much more efficient, this also lead me to make a reimman sums pi approximation which dispute not being as cool is much more accurate and practical

[@mhmd-mc113]

@@garrettrhoads6329 if you want fun ways to calculate pi, find the probability of 2 random numbers being coprime (coprime meaning with a gcd -greatest common factor- of 1)

[@garrettrhoads6329]

@@mhmd-mc113 wouldn’t you need a nested for loop to do that? is there a way that’s more efficient using recursion or something?

[@chayanaggarwal3431]

Well umm you could this by just integraring on a quarter unit circle and equate it with binomial expanded form of the same integral and then you could calculate pie on any order you want (I know what he did in the video was kind of integration only )

[@aarnavsood28]

Title says "random way to calculate pi", not the best way. There are many many ways to approximate its value and what you're saying is exactly what Newton did.

[@davidtatum8682]

I was with you for like 5 seconds. Then my brain liquefied and ran out of my nose

[@jurekis9177]

THIS kind of stuff should be in my school on Pi Day

[@clashoclan3371]

I don't think you should give computer science topics in highschool, they probably don't even know pre-calc.

[@GynxShinx]

Yeah, I did this in an Excel spreadsheet when I had nothing to do at work.

[@zachwaldron7146]

I wish i knew what he was talking about. Understanding maths seems cool

[@danielttk8682]

I'm subscribed, I need more math in my life

[@gregfeneis609]

Totally appropriate that the Pi-thagoras' theorem is used for this.

[@cy83]

Theres actually a full lengthed video made by Joma that talks about this!

[@SophieJMore]

Do points have to be randomly distributed? What if they're just arranged in a grid? Would the approximation be better this way?

[@thegodsofai3845]

Justin cracked at math!?!?!

[@gangstaflower2262]

Amazing Video !

[@gamechip06]

That's really cool

[@clxse1]

Yes , I totally agree with you.

[@diegovera4962]

Two weeks ago, I had to do just this, but in Matlab, for a university class XDDDDD. We started with 1,000 points, then 10,000, 100,000... It was satisfying to see how "our pi" got closer and closer to the real value

[@nonstopdude1211]

i had a very wonderful pi day.. you have a wonderful pi day my "points" fella

[@rajubhaimarwadi9515]

But you actually count those points??? 🤯

[@nubdotdev]

Well, my computer did :)

[@Astromath]

He wrote a script selecting a random x and y coordinate lying inside the square. Then for every point, the code checks if x²+y²

[@shanewalsch]

Write a program

[@viveck1279]

@@nubdotdev need that program code

[@prathamkalgutkar7538]

@@viveck1279 Check the Pinned Comment

[@Matthew_Klepadlo]

One interesting way that I like is Fracious Viete’s method: Taking 2, plus 2 over the square root of 2, plus 2 over the square root of 2 plus the square root of 2, plus 2 over the square root of 2 plus the square root of 2 plus the square root of 2, and yadda-yadda-yadda.

[@JustaReadingguy]

My calculator has a better appreciation with a single button.

[@misamisamisamisa]

Cool. I figured out it won't be accurate from the start. It's too random but it's pretty close.

[@Thamios]

It's more of an estimation rather a calculation

[@chingchenhanji]

I remember We did this in computer science class in high school But in excel Also Joma Tech also made an explanatory video about it Wonderful, late, Pi day everyone

[@ryantony5586]

This is a programing interview question 😂😂😂

[@_Unknown420_]

Me: yes maths My brain: 1+1=11

[@VestinVestin]

Fucking implicit type conversion...

[@fabriziobrutti1205]

At the end, the famous Pi pie

[@riceisbetterthanyou5077]

wow! this is very impressive

[@Doctor_Drew]

great video!

[@maevesilvestrys5600]

Love ❤ the video

[@jfd7090]

No it is not close... The central limit theorem shows that these Monte Carlo methods are a fast but dirty and therefore approximate way of calculating multi dimensional integrals.

[@ripleyxo631]

Pi? Numbers? What are you talking about lets get some bananas

[@henrique7149]

wow, thats so cool

[@fatitankeris6327]

Remember 3Blue1Brown making a video about this.

[@cipherxen2]

Denominator is already 3141

[@nubdotdev]

I just chose that number because it’s pi day but you could use any sufficiently large number of points and get the same result.

[@cipherxen2]

@@nubdotdev Yeah. I know.

[@alexp15-]

i thought it was peas in the thumbnail XD

[@akankshasharma7498]

I did study this in my Design and Analysis of Algorithms class

[@SophiePastelz]

Very cool,

[@Loading-lg6hs]

awesome vid

[@Loading-lg6hs]

5.62

[@abdou4alg]

I am surprised neither the video nor the comments mention that this is called Monte Carlo method

[@tofaa3668]

Here is another calculation of pi. Create a perfect world where no energy is lost on collision and have 1 wall and 2 blocks 1 x times heavier than the other, count how many back and forth collisions it makes and the number should be a x amount of digits of pi

[@pujanmodha2749]

I took just one point and i got value of pi from parallel universe

[@mlembleh5451]

Just in case if anyone want the code for this algorithm, it's written in javaScript so you can run the code in browser console . var n = 1000000; var ins = 0, outs = 0; for(var i = 0; i < n ;i++){ var x = Math.random(); var y = Math.random(); var z = Math.sqrt(x*x + y*y); if(z

[@Siwphlhths]

should i do it on the maths finals now?

[@alexvitkov]

i mean, you could just pick points uniformly, there's no need to introduce the RNG variance

[@ImZyron]

I know i'm like two months late but theres a video by The Coding Train on youtube about this where he describes all this and how to code it as proof

[@yoursleepparalysisdemon1828]

would this be better if the points were in rows, or completely random?

[@terrsus7676]

I think its funny that i knew what the method would be by looking at the thumbnail 😁

[@kienthanhle6230]

Can I make a video about testing the accuracy of this algorithms, as well as doing some optimization on it? (I will leave the credit)

[@nubdotdev]

Yeah, of course! That should be pretty interesting.

[@kienthanhle6230]

@@nubdotdev Thank you so much!

[@lerkabishhhit]

This method isn't new, it calls Monte Carlo method, and it's accuracy is pretty bad, because method error is random value, but amounts of implantations are interesting

[@kienthanhle6230]

@@lerkabishhhit yeah, I've tested it with the sample size of 10^9 and the output was an astonishing 4 correct digits. Like did I do anything wrong?

[@Llamaful]

How is it random? It literally uses a circle as the main calculation.

[@garrettrhoads6329]

The points are placed randomly in the square

[@omarel-nemr6506]

Cool

[@oli43ssen]

I lost you after you added the dots

[@jontedeakin1986]

3blue1brown influence

[@Bob78]

Nice video, but why do they need to be in random places? Why not a uniform grid. Surely that would be even closer to pi?

[@fuyalasmit]

ahh I'll better use 22/7 😌

[@onelivingsoul2962]

I have tried this in matlab and it took about 80,000 points to get to 4 digit accuracy

[@atharvapatil6003]

Veritasium and physics girl did this experiment with using darts eight years ago They published video on 14 march 2015 And the result was shocking 3.139 with almost 0.1% of approximation error Also he did with drifting a car and using physics which is not dependent on area or circumference property of circle. That's cool though. Do anyone know any other method then tell

[@Sasoon2006]

This depends on how good is "random" method implementation.

[@jeevankahlon5570]

i love pi

[@F1NALEXD]

He is speaking the Language of gods

[@deepasrip9519]

Him : we have to calculate pi by counting these dots . Me : π = circumference / diamerer

[@Exisist5151]

Aka my CS assignment last week

[@oldboyiscool4040]

Why is pi so ducking versatile, plop you there and put you there and dat shiz works for some reason

[@JwalinBhatt]

Does the numbers being "random" have any significance? What if we just took the points uniformly?

[@darkzonegaming9169]

I think by random he meant uniform, I think what I means to be uniform is if the area and the number of dots in that area are directly proportional

[@itsroman2112]

Crazy

[@goofybidoofie]

monte carlo moment

[@DerB23]

Why does the distribution have to be random? Would the result be different when using a completely even distribution in a geometric pattern?

[@tempname8263]

No.

[@yes-mu4gr]

cool

[@Dark_Matter2]

I see doggo in points

[@--2]

Now we need a proof ;)

[@leothesleepingdog6055]

I think i went s bit overboard putting in 69420 dots in there 😳

[@chickenmonger123]

What stops the “randomization” from being derived from pi in the first place? Which is easily resolved in reverse to derive pi?

[@spiderduckpig]

The randomization is not derived by pi. You can check if a point is in the circle by just seeing if x^2 + y^2 < 1 (if the radius of the circle is 1, and the center of the circle is (0, 0)).

[@Shad0wWarr10r]

Why would you even need to randomize the points instead of just making a mesh with every point 0.001 between eachother

[@easysolutions3312]

Now do this but the dots are people.

[@elitememes7268]

Did this around a year ago in computational science class tenth grade

[@megamaz108]

Tried it out myself and averaged out at 2.9 no matter the amount of points :/ nvm I forgot decimals existed.

[@BruH-xg5eo]

Pi pie...

[@gaviningrave1731]

Im just Justin Justin time for a random way to calculate pi

[@sjk7467]

Shouldn't similar things work for literally any shape? Draw a square, put any shape in, see what ratio of points fall in it, now you can calculate the area.

[@succathog5906]

Lmao I thought it was grass

[@ilham-t9y]

Pie

[@julianbrudka9821]

lol my brother just made it as college project

[@UberBossPure]

Why you use x square and y square? For what it stands? I understood r square is the circle. x*x or y*y are both getting the surface of an square. But why we use it 2 times?

[@tempname8263]

Pythagorean theorem. Look it up.