Squaring the Circle
This first appeared as an article in (n)sight magazine. (Autumn/winter 2009).
Finding a good approximation to the squared circle leads directly to an approximation for π. This gives a feel for the kind of limiting processes used by Archimedes, and which Newton and Leibnitz formalised into the calculus techniques we know today.
The article describes how you can build up this approximation from a blank Graphs & Geometry screen. The completed file is also available to download.