Circle and polygons

After the line and the related shapes produced by it, i.e. line segments, broken lines and polygons, the circle is the simplest curve which, like the line, has a certain homogeneity and shows the same behavior in all of its points and parts but, contrary to the line, it does not extend to infinity. Also, the line and the circle are the shapes for which we have the simplest drawing tools, the ruler and the compass. If we had a third, equally simple, tool for drawing a third category of curves, we would certainly include these curves also in the domain of elementary euclidean geometry.