CircumferenceEstimate.cs

using System;

namespace Sum
{
    class Program
    {
        //Estimates the perimeter of a circle of radius 1 using Archimededes formulas
        static void Main(string[] args)
        {
            int n = 96; //n-polygon to estimate with.
            double r = 1; //radius of the circle.

            double A = 1/Math.Sqrt(3); //value of A1.
            double C = 2/Math.Sqrt(3); //value of C1.
            int k = (int)Math.Log(n, 2);

            for (int i = 2; i < k; i++)
            {
                A = A / (1.0 + C);
                C = Math.Sqrt((A * A) + 1.0);
            }

            double estimate = n * 2 * A;
            double actual = 2 * Math.PI * r;

            Console.WriteLine("n = {0}, A = {1}, C = {2}", n, A, C);
            Console.WriteLine("Estimate = {0}", estimate);
            Console.WriteLine("Actual = {0}", actual);
            Console.WriteLine("Difference = {0}", estimate - actual);
        }
    }
}