Estimating Pi
The ratio of the circumference to the diameter of a circle is a constant designated by pi. Pi is approximately 3.141592, although 3.1415 and even 3 1/7 are sufficiently accurate for ordinary purposes.
Estimating pi has been an interesting diversion for the mathematics student. Even historically, the value of pi was obtained by experimentation and estimation. Archimedes described the value of pi as lying between 3 1/7 and 3 10/71.
One of the more interesting estimations involves throwing darts at a unit circle inscribed in a unit square. The area of such circle divided by the area of such square is pi/4. Therefore, four times the number of darts landing inside the circle, divided by the number of darts thrown randomly at the square, is an estimate of pi.
The following applet illustrates such a scheme to estimate pi. The number of darts is input by the user and is limited to a five digit integer.