It is a well known fact in Mathematics that Pi is 4*arctan(1). arctan(x)
is the integral from 0 to x of (1/(1+x*x)) or, if you're not
mathematically inclined, it is the area between the x axis and 1/(1+x*x)
and between the y-axis and x. So, the for loop is simulating this
integration. Of course, the better way to do this is to do a Taylor
expansion of arctan.
JDM
On Fri, 12 Mar 1999, Bal K. Paudyal wrote:
> Hello Friends,
>
> I encountered following program in one of the Linux Howtos. This calculates
> the value of pai. But how does it do this? I am not asking the programming
> details, but on what theory the formula is based on. Can anybody help? Is
> there any better place to look for help?
>
>
>
> ---------------------------------------
> #include <stdlib.h>;
> #include <stdio.h>;
>
> main(int argc, char **argv)
> {
> register double width, sum;
> register int intervals, i;
>
> /* get the number of intervals */
> intervals = atoi(argv[1]);
> width = 1.0 / intervals;
>
> /* do the computation */
> sum = 0;
> for (i=0; i<intervals; ++i) {
> register double x = (i + 0.5) * width;
> sum += 4.0 / (1.0 + x * x);
> }
> sum *= width;
>
> printf("Estimation of pi is %f\n", sum);
>
> return(0);
> }
> --------------------------------
>
>
> --
> Unsubscribe? mail -s unsubscribe [EMAIL PROTECTED] < /dev/null
>
>
