Start with a square and draw a circle inside with the same diameter as the square.  Darts can be thrown at random points onto this square. If the dart lands inside the circle, it counts as a hit.  The proportion of hits to tries is one quarter of π.  

Below is a program that has graphical representation.

{{ ::estimatepi.java |}}


[[https://mathorama.com/pisim.mov|{{:screen_shot_2018-10-02_at_7.52.17_pm.png}}]]

It takes a while to run this simulation to determine an approximate value for π.  Write a simple text only program that uses a ''for'' loop or a ''while'' loop so that can run 200,000 dart throws more quickly the the graphical version. 

This works since the ratio of the Area of a circle divided by the Area of the square is pi*r^2 / (2r)^2 = pi/4. The ratio of the darts that land in the circle divided by the darts thrown on the square should be the same ratio, pi/4 (if we throw enough random darts!). So 4 times this proportion is pi!