Our colleague Steven Strogatz has written a series of articles on mathematics, targeted to a “lay” reader, for the “Opinionator” series of the New York Times. Stogratz’s latest article reconstructs Archimedes’ discovery of how pi can be seen to be a limit of areas of inscribed and circumscribed polygons: Strogatz article on limits.
Strogatz’s other articles can be read here: Strogatz math articles.