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.
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!