Calculating Pi 2.MP4

This is the second in a series on how to calculate the numerical value of Pi. In this clip, I show how a simple series expansion lets us calculate Pi to any accuracy we like. I present two different series expression and show how one of them converges much faster than the other.

Note: At about 4:22, I state that a series is made of prime numbers. I should have said they were odd numbers.

Category:

Education

Tags:

• calculating pi
• estimating pi
• value of pi
• taylor series
• infinite series

[iamnorwegian]

I'm a cashier, and often I dont get any customers. The other day when this happened I started thinking how strange it was to calculate the length of a curved line, but I thought it was probably just an aproximation with some sort of limit function. So I started making figures liike the ones in your other video, and made a function for pi, but it looked a lot worse than yours. When I got home I typed it into my calculatin program, and it told me the answer was pi :D

I love it when math just works

[purdueMET]

@iamnorwegian That's wonderful. I was making up a function the other day for a homework problem and found, completely by accident, that the integral from -infinity to plus infinity was Pi. Clearly, it lurks everywhere.

You might enjoy some math videos by a young lady named Vi Hart. Check them out at ViHart.com. She does a great job of linking math and drawing.

[taricho]

If I may, you said something wrong verbally, when you showed the Taylor expansion of pi, you said that the series has a simple pattern made of prime numbers. The expansion has odd numbers and not prime numbers.

Thanks

[purdueMET]

@taricho Thanks. You're right; I should have said odd numbers rather than prime numbers.

[mahansal1]

pie is not exact... it's wrong math... pie is an approxiamation... not the exact value... that's why pie is wrong!

[ZorroIsGod1]

very bend you do in your calculations cost time...... its why it comes up... bend calculations...... so you over shoot pi....

[therockana]

is using arcsin 30 degrees the fastest algorithm for calculating pi..?

[FaradaysBirdCage]

Same way I learned to do it! :)

[rubikskidcube]

please make a video tutorial for Taylor seares expansion i don't get none of the videos were makeing it hard 2 understand so please! please! make a video about Taylor searies expansion! reply and tell me if u will please!

[iamnorwegian]

@purdueMET I am actually subscribed to Vi Hart here on youtube:D Her humerous and artistic twists to mathematical consepts are really entertaining, and very interesting as well. I mostly watch videos of some educational/artistic value when im here. Im glad to have come over her and your stuff.

Youre discovery sounded very interesting, but I did not quite get it. If it was a joke on a flaw in the equation I posted in the other comment, or even if it wasnt, then Id love to learn:) perhaps a video?

[iamnorwegian]

In case you wondered, this was the function:¨

pi = lim( x -> inf ) (x*sin(360/x)) / (2*sin(90-(180/x)))