# Let's talk about π.

Today I'd like to teach you all about one of my all time favorite constants: π!

Most likely, all of you know that π is the ratio of a circle's circumference to its diameter, and probably only know only 3 to 5 decimal digits of it. However, π is an irrational number, meaning it has no end! Let us go through all of the different formulae of π I have programmed, and explain what they mean! Let's dive in. (These are numbered in the order that they print when the attached code is run)

- The Monte Carlo Method

One way you can do this is by drawing a square, with a circle whose edges touch the 4 edges of that square within. Now imagine you were to draw many many dots randomly within the square-circle hybrid. If you take the number of points that fell within the circle, divide it by the total number of points, and multiply it by 4, you get (you guessed it) π!! More info can be found here:

https://ja.wikipedia.org/wiki/モンテカルロ法

- The Chudnovsky Algorithm

This is one of the fastest methods out there, being used in the world record, to calculate 50 trillion digits of π! I already explained it in a previous post, but the formula (and more cool information!) is here:

https://ja.wikipedia.org/wiki/モンテカルロ法

- The Basel Problem

This problem, posed by a man named Pietro Mengoli, asked for the exact sum of an infinite series, with proof. Mathematician Leonhard Euler answered this, with proof, finding it to equal exactly π^2/6. Further info and interesting facts here:

https://ja.wikipedia.org/wiki/バーゼル問題

- The Wallis Product

Unlike the other formulae here, this one uses the Product Operator in its equation. If repeated over an infinite number of times, it will equal π/2. More information here:

https://ja.wikipedia.org/wiki/ウォリス積

- The Leibniz Formula

Last but certainly not least, I have here probably one of the slowest π-convergent methods out there. In fact, to get π accurately to 10 decimal places takes about **5 billion** iterations, according to the Wikipedia page! This formula alternates between adding and subtracting fractions with odd denominators (meaning this is an example of an alternating series), and converges on π/4. For extra information, go here:

https://ja.wikipedia.org/wiki/ライプニッツの公式

I plan to make more π approximation programs in the future, so stay tuned if these kinds of things interest you as much as they interest me!

Thank you. ^ ^

nice job! also,congrats on geting on the leader bord!

`Chapter1:An Introduction.`

My name is Ariana Bridger.And I am the Most PowerFul Jedi in the universe.That might seem awesome. But it's really not. Because,when you're as Powerful as i am, The Sith find you easily as pie. I’m shocked my crew stayed with me.But they do.That i am glad. Because without my crew I would be dead by now.

When my master made me a full Jedi at 8 years old, everyone was shocked.That was 4 years ago. When I still used my real name. But now, everyone knows me as Adrianna luv.

I was born in an imperial prison to Ephraim and Mira Bridger. When They had to give me to the Sith, they whispered in my ear. They told me to be strong and stand up for what is right. I always remembered that. Their death is the reason for me leaving the empire, and becoming a Jedi instead of a Sith. I never thought i’d see any of my family again, But that was before I joined the Rebellion, and met Ezra Bridger. Now, to tell my story. It started when I got caught stealing a kyber crystal from the empire.

-Ariana Bridger

Wait, there are different numbers for π? This is when the confusion sets in...

I'm also very young. I don't get these things.

No, there are not multiple values for π. There is only one, that being '3.14159...' and so on. These are merely methods of calculating π, albeit with varying amounts of accuracy at certain numbers of iterations.

π is quite interesting and cool, in that it can show up within the solutions to various mathematical problems that appear to have absolutely nothing to do with circles (at least at first glance)!

The things that the program displays are not π, in that, based on the accuracy I've asked for, the digits it shows aren't EXACTLY π.

For example, a common value that we use when approximating π is 22/7. This is only accurate to 3 digits (3.14), and even closer is 355/113, which is accurate to **7 digits** (3.141592).

While they aren't equal to π, we often use them, since they are close enough to be somewhat useful for our purposes!

We don't know what π equals exactly, since it is infinitely long, but these equations can hep us learn more and more.

Here's a helpful link that non-math people can understand ^ ^

wow you beat me in only like number 5 on hot now lol

tho im confused why is this in Japanese lol

@LizFosterjust curious lol

@LizFostertime to whip out google translate lol

@LizFosterYou know there are English versions... ^ ^*

no the ~~post~~ *program* lol

Do you know anything about something called a spigot method/algorithm or something? I heard of them at some point, but I’m not entirely sure where or exactly how either...

http://stanleyrabinowitz.com/bibliography/spigot.pdf

I am a bit of a nerd when it comes to math-related subjects (as you can probably tell), so I have many articles like this waiting for use.. wwwwww

( . __ . * )

Unfortunately I don't have any books on Python or really programming in general (Lol)

*really strongly*suggest you do, it’s so awesome.

I’d suggest maybe checking out cryptography or maybe AI Books, those are pretty math heavy I think :P

Actually if you learn C++, I found this one a while back on Neural Networks:

http://www.ece.ubc.ca/~msucu/documents/programming/C++%20neural%20networks%20and%20fuzzy%20logic.pdf

I don’t know if it’s actually good I forget I haven’t picked it up in a while(again- too mathy for me I’m bad at math lol)

And then this one is on analyzing stream ciphers(which are really cool by the way)

http://www.cs.ru.nl/~rverdult/Introduction_to_Cryptanalysis-Attacking_Stream_Ciphers.pdf

Again these are kinda introductions and also just things I pulled from my library, so I don’t how good they are but I hope they are helpful. :P

https://www.youtube.com/watch?v=cqgtdkURzTE

https://www.youtube.com/channel/UC1usFRN4LCMcfIV7UjHNuQg

and then for fun (probably not as related Lol):

If P and Q are two points on an elliptic curve such that kP = Q, where k is a scalar and sufficiently large, it is computationally infeasible to obtain k if k is the discrete logarithm of Q to the base P . Note that this is computationally infeasible even if P and Q are known.

XS ohh boy. Here we go again lol.

I was summoned! Yeah, I’m a big cryptography fan! feel free to pimg me with q‘s!

@LizFoster @Highwayman@enigma_dev Nice! QnA galore! ^ ^*

@enigma_dev Oh, yay! Hi! Um, so

I was reading some stuff on the diffie-hellman key exchange, and they started discussing ECC, which I though was basically just another asymmetric encryption algorithm like RSA, but now I’m kinda confused because it started to look like it was just another form of the aforementioned diffie-hellman exchange, so I guess what my question is is what is elliptic curve cryptography?

the only cryptography i know is the Caesar shift wheel lol

@LizFosterno idea what your talking about lol

@Highwayman
Great work Liz! Very, very interesting post about a very, very interesting number! I just gave you the conzent creator role, which marks creators who upload high quality content! Congratz

@enigma_dev Oh, thank you! I really appreciate that, that is so awesome of you! Yeah, numbers like π really get me going in terms of conversation, they are just so beautiful!!

@enigma_dev Simp!

@Andi_Chin Why are they a Simp? ; - ;