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Math Help - [SOLVED] How to calculate PI

  1. #1
    Magician
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    [SOLVED] How to calculate PI

    Hi Every bdy

    please how to PI that equal 3.14
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  2. #2
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by Magician View Post
    Hi Every bdy

    please how to PI that equal 3.14
    Are you asking how to find \pi?
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Magician View Post
    Hi Every bdy

    please how to PI that equal 3.14
    See this thread.

    RonL
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  4. #4
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    CaptainBlank 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 \sqrt{r^2-x^2} is a circle with radius r. So the area below it is,
    \int_{-r}^r \sqrt{r^2-x^2}dx=\pi r^2
    Setting r=2 and some manipulation,
    \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 \pi.

    Another was is to use an infinite series,
    \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 \pi but way too slow.

    A quicker one I can imagine was proven by Euler, the Basel problem,
    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.
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by ThePerfectHacker View Post
    CaptainBlank 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 \sqrt{r^2-x^2} is a circle with radius r. So the area below it is,
    \int_{-r}^r \sqrt{r^2-x^2}dx=\pi r^2
    Except that it give the area of a semi-circle, you mean something like:

    <br />
\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 
    >
    RonL
    Last edited by CaptainBlack; November 17th 2006 at 08:11 AM.
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  6. #6
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    you can also calculate PI using the Monte Carlo simulation method and the Buffon niddle problem.
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  7. #7
    Senior Member TriKri's Avatar
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    here is another thread discussing different methods of calculating \pi.
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