Imagine a floor marked with many equally spaced parallel lines and a thin stick whose length exactly equals the distance L=1 between the lines. If we throw the stick on the floor, the stick may or may not cross one of the lines. The probability for a hit involves π. This is surprising since there are no circles involved; on the contrary, there are only straight lines. If we repeat the experiment many times and keep track of the hits, we can get an estimate of the irrational number π. (We also consider sticks of length L>1.)

The problem can easily be done as an exercise in a first calculus course, where the students are challenged to consider concepts such as probability, definite integration, symmetry, and inverse trigonometric functions. The solution to this problem therefore gives many applications in a variety of fields in calculus.

We continue by throwing regular polygons of different sizes, increasing the number of edges, and at last reach the ultimate goal of throwing circular objects. This article illustrates the process of throwing sticks, polygons, and circles analytically and graphically, and how to carry out calculations for different n-gons. The result always involves the number π, except when the circle is introduced! We also show the circle result as a limiting value as n increases to infinity.