Draw a square with an area of PI sq. units

          Area of square = 3.14159265 sq. units (PI sq. units)
          Side of square = 1.77245385 units
      Diagonal of square = 2.50662827 units

A circle drawn around it will have the following dimensions

        Circle diameter = 2.50662827 units
          Circle radius = 1.25331414 units
            Circle area = 4.93480220 sq. units
          Circumference = 7.87480497 units

                    Now, multiply the area of the square by 10,000,000

                             Giving the square the following dimensions

        Area of square = 31,415,926.5358979 sq. units (PI sq. units)
        Side of square = 5,604.9912164 units
    Diagonal of square = 7,926.6545952 units

                             And the circle the following dimensions

       Circle diameter = 7,926.6545952 units
         Circle radius = 3,963.3272976 units
           Circle area = 49,348,022.0054468 sq. units
         Circumference = 24,902.320 units

    And our earth's circumference = 24,901.463 miles [2]       Difference = 0.003442 %

If our current mile was just 2.1878 inches shorter the match would be exact!
Clearly, our mile has been an accurate geodesic measure for a long, long time.

 References:

1.  Earth,Pi,Miles and Barleycorns. Accessed 15 July 2006
      < http://hometown.aol.com/franklinhh/epmb.html>

2.  Earth - Wikipedia, the free encyclopedia. Accessed 15 July 2006
     <http://en.wikipedia.org/wiki/Earth>