N-Sided Circle?

Draw a circle of diameter 1. Using the polygon script function in GSP, inscribe an equilateral triangle inside the circle. Measure its perimeter. Repeat this process with polygons with an increasing number of sides. (There are scripts to inscribe a square, a pentagon, an octagon, and a seventeen-gon.) What can you say about the perimeters of these polygons when you compare them to the circumference of the circle? Repeat this investigation with a circle of diameter different from 1.

Extension
Is a circle a polygon? If it is, explain why. If it is not, explain what type polygon it most closely resembles.