Hi Every bdy
please how to PI that equal 3.14
CaptainBlank post is not ideal because it is speaking how to find a fraction.
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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.
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.
RonLCode: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 >