An Exposition of Polygonal Approximation of Circle

This article attempts to discuss a journey of creating an infinite number of circles from a single circle, using its tangents with a pattern ( PX; X≥3 ) and reaching uptoasingle point fromagivencircle. The time to get a newcirclefromits predecessor circle varies with the pattern. The pattern behind both the radius of the successor circles and predecessor circles is also discussed. Most interestingly, when we apply the P∞ pattern, then all the infinitely many successor circles almost merge into a single one, almost without taking any time and it takes infinite time to reach up to a single point from the given circle, for that pattern. This whole idea can be applied to astronomical objects. Although we are dealing with a circular path, which is an approximation for the elliptical orbit of a celestial body.