How is pi calculated to trillions of digits?

You know 3.14159265... but how do we calculate these digits in the first place? Measure it? Well, definitely not up to trillions of digits of accuracy, and Archimedes' method is insanely slow for trillions of digits to be calculated. Here is a simple explanation of Machin-like algorithms, which only requires high school knowledge of complex numbers.

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[mathemaniac]

I put a lot more effort into making this video, particularly on the research part, as you can tell when you read the description, and you should read links in the description if you are interested - you will learn a lot more:)

[OscarVeliz]

On Jan 29th, three weeks after this video was posted, the record for π was broken. It is now 50 trillion digits. Congrats on 1k subscribers! *edit* I subscribed too.

[LesleLeBang]

-Take the first three odd integers: 1, 3, 5
-Double them thusly: 113355
-Divide the last three by the first three thusly: 355/113
There ya go, Pi accurate to 6 decimal places!

[etaung_]

This was simple, short and informative. And incredibly helpful.

[christinehelenbeard]

I am looking for a video on pi for an elementary algebra student. This is too complex for him right now, but I found it fascinating. Beautifully done!

[TheUltimateSay]

This is concise and on-point. Good job

[gruber]

You deserve way more attention! Great Video!

[YASH-bswu]

I have a question....
How do they verify that each digit of the trillion digits are correct?

[abbasmehdi]

You are the one that i want to be my mathematics teacher. Most interesting vedios on youtube is only your one's. Plz always upload vedios similar to this..I gain much knowledge than my traditional
Mathematic books.

[monketeachmonkelearn]

This may be a silly question but I am truly trying to understand. How do we know that these equations work when we don't know the exact numbers pi consist of? Is it declared true based off of the validity of the properties of the equation rather than the end number?

[wilamlu]

But how did they implement the algorithm with programming language like C, with limited precision?

[urgjendevetak]

the fourth special product u wrote is wrong. It should be (5, 1)^4 * (2, 2)^(-1) = (239, 1)

[martebest]

Interesting and deep explanation. Thanks a million. Then maybe you will understand. Please consider it. We have some tricky formulas to use to calculate the value of Pi. In my opinion, the value of Pi can be calculated in a much easier way. We have the formula Pi = Phi^2 + RC . Phi is the golden number, RC (royal egyptian cubit) is Pi/6 so we have Pi = Phi^2 + Pi/6 and hence Pi - Pi/6 = Phi^2 and then 5*Pi = 6*(Phi^2) so Pi = 6*( Phi^2)/5 We know that we can get a good approximation of Phi by dividing the largest possible values ​​of the Fibonacci series. The values ​​of the sequence can be calculated using the formula: f(n)=f(n-2)+f(n-1) so let's take this notation let's substitute it to calculate Phi, so Phi = f(n) / f(n-1 ). I substitute these values ​​into the formula and we have Pi = 6 * ( f(n) / f(n-1) )^2) / 5 So this is another and rather new formula for calculating the value of Pi. Do you understand? There was no such formula before to calculate the value of Pi. Maybe you should nominate me for the Abel Prize? 😁 Maybe aliens will come to shake my hand after all... 😜

[pigman]

machin method seems so much simpler... why is it that the chudnovsky method is typially used? it seems like it'd take much longer to compute..

[reapersgamingyt]

What is the digit value of pi or how to find it

[nareshrikhari]

Great videos bro...I hope your subscribers increase to the number of decimals in π(pi)!😃

[harishinstitute]

Please send me some more link to explore Pie

[geluklu]

you are a great youtuber ı was thinking making a video like this but the differnce is ı write program for that and was gonna intorduce it
it can calculate 30 decimal places and it can kept going but when time passes program begun to beign really slow
it uses nilkantha method and write in c++ ı didnt make the vid yet but i will soon.

[SuryaBudimansyah]

Where can I watch this "year's worth of videos" ?

[JOHN-tkvl]

So they spend millions on computers that can calculate Pi
to trillions of decimal places. For what?