PrintPI.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;

namespace PrintPI
{
    class Program
    {
        static void Main(string[] args)
        {
            //Console.WriteLine(2 * F(1));
            string lines = GetPi(10000, 100).ToString();
            int nInterval = 50;
            string res = String.Concat(lines.Select((c, i) => i > 0 && (i % nInterval) == 0 ? c.ToString() + Environment.NewLine : c.ToString()));
            Console.WriteLine(GetPi(10000,100).ToString());
            System.IO.File.WriteAllText(@"C:\Users\Isham Mohamed\Desktop\PI.txt", res);
            Console.ReadLine();
        }

        public static BigInteger GetPi(int digits, int iterations)
        {
            return 16 * ArcTan1OverX(5, digits).ElementAt(iterations)
                - 4 * ArcTan1OverX(239, digits).ElementAt(iterations);
        }

        //arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + x^9/9 - ...
        public static IEnumerable<BigInteger> ArcTan1OverX(int x, int digits)
        {
            var mag = BigInteger.Pow(10, digits);
            var sum = BigInteger.Zero;
            bool sign = true;
            for (int i = 1; true; i += 2)
            {
                var cur = mag / (BigInteger.Pow(x, i) * i);
                if (sign)
                {
                    sum += cur;
                }
                else
                {
                    sum -= cur;
                }
                yield return sum;
                sign = !sign;
            }
        }
    }
}