Project Ideas

I've stumbled on an interesting coder's project ideas list



Then tackled the first one in my own way. The goal is to

Find PI to the Nth Digit – Enter a number and have the program generate PI up to that many decimal places. Keep a limit to how far the program will go.


Rather than do exactly that, I wanted to start small, and work through some of the existing formulas I could find and put them into C#. That would be a step in the right direction towards the goal. I think the actual project idea is currently out of my range, with little to gain from going farther than I did. I learned much more about floating point math, decimal vs. double, and binary vs. decimal vs. hexadecimal math.


Code Follows:

/// <summary>
  /// http://en.wikipedia.org/wiki/Pi
  /// </summary>
  /// <seealso cref="http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems"/>

public static class PiCalculator
  {
    /// <summary>
    /// http://en.wikipedia.org/wiki/Numerical_approximations_of_%CF%80
    /// </summary>
    /// <returns></returns>
    public static double Euler( )
    {
      return 20*Math.Atan((double)1/7)+8*Math.Atan((double)3/79);
    }
    public static double MachinLike( )
    {
      return 4*(4*Math.Atan((double)1/5)-Math.Atan((double)1/239));
    }
    public static double Archimedes1( )
    {
      double archimedes1=0;

      //most accurate number this formula can give on a computer
      const double magicNumber = 16;

      double previousT=1.0/Math.Sqrt(3.0);
      for (double i = 0; i<magicNumber+1; i++)
      {
        archimedes1=6.0*Math.Pow(2.0, i)*previousT;
        previousT=(Math.Sqrt(Math.Pow(previousT, 2.0)+1.0)-1.0)/previousT;
      }
      return archimedes1; //gives the expected 8 digits of precision 
      // 3.1415926 wrong digits - 7174155

    }
    public static double Archimedes2( )
    {
      //most accurate number this formula can give on a computer
      const double magicNumber = 23;
      double archimedes2 = 0;
      double previousT=1.0/Math.Sqrt(3.0);
      for (double i = 0; i<magicNumber+1; i++)
      {
        archimedes2=6.0*Math.Pow(2.0, i)*previousT;
        previousT=previousT/(Math.Sqrt(Math.Pow(previousT, 2)+1)+1.0);
      }
      return archimedes2; //returns 13 digits of precision instead of the expected 15
      // returns 3.1415926535898 instead of 3.14159265358979

    }
    /// <summary>
    /// http://pi.lacim.uqam.ca/eng/approximations_en.html
    /// </summary>
    /// <returns></returns>
    public static double Plouffe()
    {
      return Math.Log10((double) 28102/1277)*(double) 125/123;
    }

    public static double Plouffe2()
    {
      return Math.Pow(276694819753963.0/226588, 1.0/158.0)+2.0;
    }

  }