A Random Way to Calculate Pi

[@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

[@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

[@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.

[@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

[@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.

[@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

[@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

[@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.

[@Lore_play1]

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

[@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?

[@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.

[@pafnutiytheartist]

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

[@Llamaful]

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

[@garrettrhoads6329]

The points are placed randomly in the square

[@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?

[@josephpress.]

Python visualization (you need the turtle module) import sys sys.setExecutionLimit(60000) import turtle import random dart = turtle.Turtle() wn = turtle.Screen() wn.setworldcoordinates(-1,-1,1,1) dart.up() dart.tracer(200) numdarts = 10000 insideCount = 0 for i in range(numdarts): randx = random.uniform(-1, 1) randy = random.random() * 2 - 1 x = randx y = randy # Move to position dart.goto(x, y) # Colour red if within dartboard and count. Otherwise colour blue. if dart.distance(0,0)

[@__________________________hi52]

I know this is not meant to be the simplest way but i use ((-0.5)!)^2 which is exactly pi, the factorial of -0.5, squared

[@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

[@revenevan11]

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

[@Inderastein]

Infinite balls in the circle=Area of the circle Infinite balls inside the square=Area of the square Area of the circle/Area of the square=π/4 4(area of circle/area of square)=pi 3.14159265...=Pi

[@megamaz108]

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

[@Thamios]

It's more of an estimation rather a calculation

[@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

[@yuma9325]

commenting for the algorithm, this is some amazing stuff!

[@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

[@thecandybarbandit]

Imagine losing count of your dots

[@Snoozy_FTW]

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

[@drenz1523]

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

[@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.

[@joeylawn36111]

355 ÷ 113 gives you Pi to an accuracy good for most purposes. This is ~0.000000267 greater than π.

[@GWCGamingwithChittaarth]

This only works if you take a bit over 3000 and below 3143

[@misteick]

Code ?

[@fatitankeris6327]

Remember 3Blue1Brown making a video about this.

[@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

[@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

[@onelivingsoul2962]

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

[@ryantony5586]

This is a programing interview question 😂😂😂

[@Shad0wWarr10r]

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

[@nonstopdude]

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

[@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?

[@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.

[@frankineskinecense]

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

[@alexvitkov]

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

[@Well___hello]

In what what world 3.1415… is very close to 3.1429… ??

[@pujanmodha2749]

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

[@yoursleepparalysisdemon1828]

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

[@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

[@FM1234]

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

[@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.

[@davidtatum8682]

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

[@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.

[@Sans________________________96]

Draw square with 𝝅 A green dots Draw circle It’s 𝝅

[@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

[@ababwe7657]

I am not smart enough to understand this

[@mayonster4798]

Or hear me out, you take a circle with the diameter 1. Boom your circumference is pi

[@leothesleepingdog6055]

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

[@ilham-t9y]

Pie

[@abdou4alg]

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

[@ripleyxo631]

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

[@catwithshades7577]

I didn't see anything inside. Am I colorblind?

[@JustaReadingguy]

My calculator has a better appreciation with a single button.

[@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.

[@gaviningrave1731]

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

[@tomasugarte1205]

if its on the line?

[@darkzonegaming9169]

We can safely ignore them as those dots don't contribute to the area of the circle and aren't needed in the calculations, as the number of dots go to infinity the proportion of points on the line go to 0 (I think)

[@elitememes7268]

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

[@codyx8273]

Shouldn’t it be D squared and not R squared?

[@jellybeaniac152]

Yes ( I understood nothing)

[@mrtank2010]

me a 5th grader this makes no sience

[@Ahris_aus_der_8._Dimension]

Mhh, i have tryed it with 100 mio. points several times. the best wars 3.14164.

[@MrTrogdor2099]

Damn that's pretty bad. Might be good to use a better random function

[@tungduong5179]

i can just put 1 point outside the circle and pi would equal 0

[@sploofmcsterra4786]

Why a random distribution over a uniform one?

[@_Unknown420_]

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

[@VestinVestin]

Fucking implicit type conversion...

[@littlebabypuffer]

until x == pi { x = Math.Random };

[@oholaoholiba6467]

is pi a mutyplier or just random summary? 😇

[@mathiusr218]

JESUS loves you 🙏🏻🙏🏻🙏🏻

[@thegodsofai3845]

Justin cracked at math!?!?!

[@alex-h3x1b]

i thought it was peas in the thumbnail XD

[@cariboubearmalachy1174]

3000 randomly generated points and 3000 boolean calculations to get accuracy to 2 decimal places? You only need 2 or 3 terms in a Maclauren series to get the same level of accuracy.

[@keonscorner516]

*3141

[@tempname8263]

That's just one of the ways. No need to complain about this way even existing, lol

[@jakerussell135]

if you know how to find the area of a circle, it makes perfect sense, even without watching the video and just using the thumbnail

[@F1NALEXD]

He is speaking the Language of gods

[@easysolutions3312]

Now do this but the dots are people.

[@Siwphlhths]

should i do it on the maths finals now?

[@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

[@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.

[@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

[@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.

[@fabriziobrutti1205]

At the end, the famous Pi pie

[@oli43ssen]

I lost you after you added the dots

[@fuyalasmit]

ahh I'll better use 22/7 😌

[@nexusmas9]

You're cracked at fortnite

[@georhodiumgeo9827]

Why would you need random points? Just tile a finite grid, that way there would be no random fluctuations. The precision would still increase with the number of points. The randomness doesn’t “buy” you any extra precision, it seems like you think that’s helping but it’s hurting. You’re precision is the same but then you add the random fluctuations on top of that.

[@spiderduckpig]

It's called a monte carlo simulation and it's very famous.

[@georhodiumgeo9827]

@@spiderduckpig Yeah I get that but this is literally the worst place for monte carlo simulation. Think about it this way, Fill a grid with dots evenly spaced and do the same thing. You would get the same answer BUT there are no random fluctuations. Typically monte carlo simulations are used where you have a multidimensional function (higher than 2 that we have here). If you have a high dimensional data set it isn't possible to simulate every value in every dimension so if you grab a distribution of random inputs you will see a good representation of "likely" outputs. There is nothing "likely" about Pi, it just is what it is. If you did a thousand points with monte carlo you would find that Pi is PROBABLY near 3.14 plus some precision errors. If however you did this on an even grid you would find that Pi IS 3.14 plus some value past your precision. You have the same precision just without the uncertainty. It's just a bad use for this tool.

[@spiderduckpig]

@@georhodiumgeo9827 Yes, it's a very time-consuming and inefficient demonstration, but it is just a demonstration. Obviously the creator could just use one of the many different series that converge to pi quicker if they really wanted to quickly find pi, or one of thousands of others of better methods. But the point is that it's a very simple and easy demonstration, so this exact example shows up in a lot of introductory CS classes. Of course it wouldn't be hard to code a grid of points like you suggested, but it would be even easier to randomly place points.

[@georhodiumgeo9827]

@@spiderduckpig I must have misunderstood the video. I see now, it's like one of those life hack videos where somebody turns a sponge into a bad shoe. I agree, this is a horrible way to find Pi and also if you wanted to do it this way it's also a bad implementation of how to do the bad way of doing it. Thanks for the clarification, It just seemed like an unnecessary complicated way to do it badly. I guess I'm bothered that so many programmers are entering the workforce with tools they don't understand. I personally watched a coworker do some monte carlo simulation on a function that did not require it in any way. It was just a min-max problem that got nuked for no reason. The office walked around with a new buzzword for a week while I had to make sure, in the worst case, the equipment would work within parameters.

[@zijunryanmeng3921]

If you can draw a circle, woudn't you know pi already.

[@clashoclan3371]

But who can draw a circle, like a perfect one.

[@deepasrip9519]

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

[@succathog5906]

Lmao I thought it was grass

[@Envengerx]

How would you draw a circle programmatically without knowing the value of PI?

[@blobfish1649]

Shhhh

[@tengraint]

that's the thing, you don't. you just pretend there is one.

[@MrTrogdor2099]

You never draw the square, or the points, or the circle. You randomly generate their coordinates within the square (center of the square is 0,0, top-left is -R,R, top-right is R,R, bottom-left is -R,-R, bottom-right is R,-R). So your Xs and Ys will both be in the interval [-R,R].A circle centered at 0,0 and radius R is defined by points that follow x^2 + y^2 = R^2 . So your points are inside the circle if they are less than (or equal to) R away from the center, x^2 + y^2

[@grande1900]

0:06 SHREK!

[@gangstaflower2262]

Amazing Video !

[@jontedeakin1986]

3blue1brown influence

[@anandunambiar1032]

Poda