This applet studies the effects of inscribing or circumscribing regular polygons in the unit circle. By itself, it may add to a student's intuition about the limit concept, but It is best used after the students have learned Archimedes' theorem on the area of the circle (T.E. Heath, The Works of Archimedes, Dover Publications, p. 91). This theorem, I believe, is the most intuitive case of the limit concept, although Archimedes does not explicitly use the concept in his proof. The inscribed polygons can not cross the circle; the circle really is their limit. Similarly with the circumscribed polygons. The use of the limit concept in the definition of continuity is much less intuitive, especially on first exposure, and the purpose of the "Area" graph is to bridge that gap.
