Vieta's Formula

Vieta's Formula for

We continue the discussion on approximating by calculating the areas of a circle using inscribed and circumscribed regular polygons. We illustrate Vieta's formula, developed in 1593, the oldest exact result derived for .

The Formula

Vieta's formula expresses as an infinite product of nested square roots.

Here is the implementation:public class Vieta {

public static double rhs(int n) {
double result = 0;
double rhs_1 = 0;
double rhs_2 = 0;
for (int i = 1; i <= n; ++i) {
if (i == 1) {
result = Math.sqrt(0.5 + 0.5 * Math.sqrt(0.5));
rhs_1 = result;
rhs_2 = result;
} else if (i == 2) {
result = rhs_1 * Math.sqrt(0.5 + 0.5 * rhs_1);
rhs_1 = result;
} else {
result = rhs_1 * Math.sqrt(0.5 + 0.5 * rhs_1 / rhs_2);
rhs_2 = rhs_1;
rhs_1 = result;
}
}
return result;
}

}

I also wrote a Applet for calculating PI.
http://www.myjavaserver.com/~torotime/vieta_formula.html
However,once I finished this applet, I have a new ideal that I can write it in javascript for more portable result...
applet sight~~~