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How is the value of pi derived?

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Originally posted by: Syringer
Originally posted by: b0mbrman
By measuring using bigger and bigger circles 🙂

Actually, one real way that I remember is 4 - 4/3 + 4/5 - 4/7 + 4/9...
Click to expand...

That's cool. I just tried summing up 100 terms using that on my TI-89, and got 3.13159.

1000 terms gets me 3.14059. Anything bigger takes way too long..
Click to expand...

FYI, 10000 terms gets you 3.14S1P5I9D2E6R535897932
 
Originally posted by: Syringer
Originally posted by: b0mbrman
By measuring using bigger and bigger circles 🙂

Actually, one real way that I remember is 4 - 4/3 + 4/5 - 4/7 + 4/9...
Click to expand...

That's cool. I just tried summing up 100 terms using that on my TI-89, and got 3.13159.

1000 terms gets me 3.14059. Anything bigger takes way too long..
Click to expand...
The simplification of the arctan series. It's actually exactly pi, when fully evaluated. Unfortunately, it is also terribly inefficient as far as a series is concerned.
 
an interesting "computer sciencie" way of approximating pi is to create a program to randomly generate points in a square of arbitrary length. you then inscribe a circle in that square and find out how many points are in or on that circle (just use the distance from the center of the square). pi should then approximate to:
pi = 4 * (points in circle) / (total points in square)

the more points your generate, the better the approximatio.
 
Originally posted by: dullard
Originally posted by: mygumballs
the more points your generate, the better the approximatio.
Click to expand...
Interesting, please tell more. Do you have a link?
Click to expand...

no, a friend of mine just told me about it. but a sort of proof is easy. the ratio of points in teh square to the points in the circle is the same as the ratio of the area of the circle to the area of the square. if the square's sides are x long, then its area is x^2 and the area of the circle is 1/4 pi x^2. therefore the ratio is 1/4 pi.

here's some pseudocode of the process:

int p = 0
for (int i = 0, i < n, i++)
{
x = (random number between 0 and 1 )
y = (random number between 0 and 1 )

if ( squareroot( x^2 + y^2 ) <= 1 )
p++
}
pi = 4 * (p / n)


you choose how big of n you want
 
Originally posted by: dullard
There are dozens and dozens of ways. Here is a fun method. It is quite powerful at calculating all types of things, but it is slow and inefficient.
Click to expand...

Dang you for beating me to the Monte Carlo simulation method.

And to all the morons who didn't understand the OP... PWNED! It was pretty obvious the OP was asking how to compute "pi", not what it is. 😀
 
Originally posted by: mygumballs
no, a friend of mine just told me about it. but a sort of proof is easy. the ratio of points in teh square to the points in the circle is the same as the ratio of the area of the circle to the area of the square. if the square's sides are x long, then its area is x^2 and the area of the circle is 1/4 pi x^2. therefore the ratio is 1/4 pi.
Click to expand...
Time to replace your sarcasm and repost meters. Both are malfunctioning today. I posted that exact solution already in this thread.

I lumped your repost reponse with Goosemaster's repost response for a reason.

 
Originally posted by: oboeguy
Originally posted by: dullard
There are dozens and dozens of ways. Here is a fun method. It is quite powerful at calculating all types of things, but it is slow and inefficient.
Click to expand...

Dang you for beating me to the Monte Carlo simulation method.

And to all the morons who didn't understand the OP... PWNED! It was pretty obvious the OP was asking how to compute "pi", not what it is. 😀
Click to expand...

oh teh nooeeeeeees! i didn't even know some one already posted that method already. now my posts are obsolete...🙁
 
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