How to derive a formula for π

A link to the full video is at the bottom of the screen.

That video explores how this question leads to a quandary on prime numbers, and how a pattern in primes allows for a clean final answer.

Editing from long-form to short by Dawid Kołodziej

[lombre]

"edging yourself with nothing more than a pencil a piece of paper and a formula for computing pi"

[redbiscuit-brawlstars]

When i want to feel stupid, i watch a 3 blue 1 brown video.

When i want to feel smart i rewatch a 3 blue 1 brown video.

[dividedfox]

Love these shorts! They’re a breath of fresh air compared to the rest of the brainrot most shorts consist of.

[evenh]

I love the esoteric programming language "piet". You can code in piet in ms paint. Different changes in hue and darkness/lightness define different operations and the area of a drawn area is equal to the value of the integer you put on the stack. So to calculate pi, you can draw a huge circle and put that area on the stack, then divide it twice by an area of width 1 drawn next to the circle to match the radius. The best part is that you can improve the approximation by literally drawing a larger circle.

[johnchessant]

the pi creature asking "who am I really?" haha

[llawliet]

Wow. Beautiful animation, even if I have no clue what's going on

[CreationStation.]

Thank you for making these short form videos, they always catch my attention, get me to watch the full video and get me to learn something new.

[Forever._.curious..]

The only kind of short should exist in my feed

[brandaohimself]

That little highlight of the video link is about to be meta. That was very cool

[V-for-Vendetta]

I hate how youtube isnt allowing mobile users to directly click on links in the description. I hope they're not trying to combat the idea of shorts leading into longer videos.

[tay-lore]

If this channel has taught me anything, it's that there are no end of whacky questions which seem to have no relation to circles, that when answered will end up leading you to some rational number scaling pi. Let's prove that there are infinite ways to unwittingly derive pi

[bluephoenix]

I love how you had us, as pi ask what we are. 10/i^2

[Entropy]

Yep in computer science we always love to come up with new weird ways of calculating pi. You were about to mention pi being the ratio between the points outside/inside the circle. I've seen some problems where a quarter of a circle is used for simplicity/ease of calculation since its the ratio we are looking for - whether its a quarter or a whole circle inside of a box is irrelevant.

[underscoreN]

Back in my calculus course, I remember one exam question involves solving an integral, using Taylor series to represent the function and integrate; and finally representing pi with an infinite sum. I guess that’s one way of doing it 😂

[younscrafter]

2:55 you already have a different approach to me. My approach was to find a function where you plug in x and t (amount of iterations) and it gives you a probability distribution of what y could be

[bizuplays]

Or you can expand the function of a unit circle x^2+y^2=1 except solve for y = sqrt(1-x^2) which will give you a semicircle since -y values are imaginary, expand using the binomial theorem and take the integral from 0 to 1 and multiply by four since area is pi and you calculated a quarter circle. this is the newtons way

[SvenBro]

The funnies method i have recently seen is the monte carlo method. Basically you generate two equally distributed random numbers x and y between 0 and 1. Count N one up. If x^2+y^2<1 add M one up. Repeat as long as you want. Pi equals M/N for N to infinity.

[Mike-kqyc]

I think he took the paper and pencil as an example for (ancient) mathemticians who were seeking for a formula of pi without having the power and speed of digital computing resources we posses today.

[DrBrangar]

For future reference, the little box you put to highlight the link I think is a bit more phone size dependent, cuz it just ended up flashing near the short title for me, not the link

[redfoxartist]

use a quadtrees with points in each corner and in the middle, so you subside it until all the points are inside or outside the circle, then you compute the area of squares and use the formula for area of circle, to get the area. sounds like the same thing with extra steps, but it iss way more eficient