The Pi of Archimedes
This blog began life more than two decades ago, as part of a series of lectures I delivered to some very bright first-year engineering students at an Australian university. The number π (pronounced ‘pie’) has been recognized from time immemorial because its physical significance can be grasped easily: it is the ratio of the circumference of a circle to its diameter. But who would have thought that such an innocent ratio would exercise such endless fascination because of the complexities it enfolds? Not surprisingly, some high school students I met recently wanted to know more about π and how it got its unusual value of ²²⁄₇. Accordingly, I have substantially recast and refreshed my original presentation to better accord with the form and substance of a blog. The online references have also been updated to keep up with a rapidly changing Web. My original intention was to write a single blog on π. But because I did not want it to become yet another overly long slog, I have decided to divide the material into two parts.