An Exposition of Polygonal Approximation of Circle

In this article, it is attempted to discuss how do we can create an infinite number of circles from a single circle, using its tangents with a pattern ( PX; X≥3 ) and what is the process to reach up into a single point from a given circle. The time to get a new circle from its predecessor circle can be reduced just by changing 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 of tangents on the single circle, then all the infinitely many successor circles merge into a single one, almost without taking any time and it takes infinite time to reach up into a single point from the given circle, for that pattern. In the whole process, polygonal approximation and sequences play a vital role.