Pi

In C# programs, pi is available in the Math.PI constant. Further, pi can be computed with an algorithm. But this is rarely needed.

Using pi in your program is not your main goal here, but finding ways to acquire its value is useful. Here we look at ways to get pi.

Example

Here we access the double PI. Include the System namespace and then call the Math.PI composite name. Math.PI here returns a double equal to 3.14.

using System;

class Program
{
    static void Main()
    {
        double pi = Math.PI;
        Console.WriteLine(pi);
    }
}
3.14159265358979

Example 2

Here we calculate pi. This program is basically never useful in a real-world program. It has no advantage over using Math.PI. It shows the algorithm implementation.

Here The PI method is called. Then PI calls the F method and multiplies the final result by 2.

Also We calculate half of pi. The F method receives an integer that corresponds to "k" in Newton's formula.

And It proceeds until it has been called 60 times, which is an arbitrary limit I imposed.

Detail Here these methods are called and the result is written to the screen up to 20 digits. The const Math.PI is also written.

using System;

class Program
{
    static void Main()
    {
        // Get PI from methods shown here
        double d = PI();
        Console.WriteLine("{0:N20}", d);

        // Get PI from the .NET Math class constant
        double d2 = Math.PI;
        Console.WriteLine("{0:N20}", d2);
    }

    static double PI()
    {
        // Returns PI
        return 2 * F(1);
    }

    static double F(int i)
    {
        // Receives the call number
        if (i > 60)
        {
            // Stop after 60 calls
            return i;
        }
        else
        {
            // Return the running total with the new fraction added
            return 1 + (i / (1 + (2.0 * i))) * F(i + 1);
        }
    }
}3.14159265358979000000
3.14159265358979000000

Newton

Isaac Newton spent a long time calculating pi to 15 decimal places. You can see that the equation defines half of pi as the sum of a fraction, expanded from 0 to infinity.

Info The result of the formula becomes increasingly accurate the longer you calculate it.

We used the Math.PI constant. We then saw a way to calculate the value of pi. We learned about double precision and the string format patterns for decimal places.