Hi Every bdy

please how to PI that equal 3.14

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- Nov 17th 2006, 06:07 AMMagician[SOLVED] How to calculate PI
Hi Every bdy

please how to PI that equal 3.14 - Nov 17th 2006, 06:10 AMQuick
- Nov 17th 2006, 06:55 AMCaptainBlack
See this thread.

RonL - Nov 17th 2006, 07:47 AMThePerfectHacker
Captain

**Blank**post is not ideal because it is speaking how to find a fraction.

---

The way mathematicians did it is by an infinite series of an integral.

If you are familar with some Calculus, the curve $\displaystyle \sqrt{r^2-x^2}$ is a circle with radius $\displaystyle r$. So the area below it is,

$\displaystyle \int_{-r}^r \sqrt{r^2-x^2}dx=\pi r^2$

Setting $\displaystyle r=2$ and some manipulation,

$\displaystyle \int_0^2 \sqrt{4-x^2}=\pi$

You can calculate the integral on the top by means of an approximation and you have a value of $\displaystyle \pi$.

Another was is to use an infinite series,

$\displaystyle \frac{\pi}{4}=1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+...$

But this series discovered by Leiniz converges too slowly, that means it does approach the value of $\displaystyle \pi$ but way too slow.

A quicker one I can imagine was proven by Euler, the Basel problem,

$\displaystyle 1+\frac{1}{2^2}+\frac{1}{3^2}+...=\frac{\pi^2}{6}$

But one of the most quickest converging series came from Ramanjuan, it is not as elegant looking as the ones above but it is far more efficient. I think each term add about 10 decimal places. So maybe this is the one that is programed into a computer to find decimal places. - Nov 17th 2006, 07:53 AMCaptainBlack
Except that it give the area of a semi-circle, you mean something like:

$\displaystyle

\int_{0}^r \sqrt{r^2-x^2}dx=\pi r^2/4$

but this is of no use if you don't know calculus.

Code:`This is EULER, Version 2.3 RL-06.`

Type help(Return) for help.

Enter command: (20971520 Bytes free.)

Processing configuration file.

Done.

>dx=0.01

0.01

>x=dx/2:dx:1;

>

>y=sqrt(1^2-x^2);

>

>Pi=sum(y)*dx*4

3.14194

>

- Dec 1st 2006, 11:36 AMWeeG
you can also calculate PI using the Monte Carlo simulation method and the Buffon niddle problem.

- Dec 1st 2006, 12:40 PMTriKri
here is another thread discussing different methods of calculating $\displaystyle \pi$.