What Is Pi, and Why Is It So Important?

[Johnh]

I can well believe that we can calculate pi to these extreme accuracies now. But I'm more fascinated by how Archimedes did it by polygons inside and outside the circle, of increasing numbers of sides and so approching a circle by geometry. And that's easy enough for us now. But how did HE work the numbers? eg how to calculate square roots in ancient Greece? if he needed to?

In fact, how did they even think about and multiply numbers? Did they have something like the Roman system , but earlier? It's not easy for doing maths with!