Inscribed Polygons Approaching Circles: A ComputationalStudy

Think a triangle is far from a circle? Our computational analysis reveals a surprising truth: aninscribed triangle already captures over 82% of a circle’s circumference. This paper delves into thefascinating progression, demonstrating how the perimeter of a regular polygon swiftly and asymptot-ically converges to that of its encompassing circle as sides are added. Using a detailed computationalmodel, we provide compelling numerical evidence of this geometric efficiency, charting the path froma mere 82.7% for a 3-sided polygon to near perfect alignment. We also precisely quantify edgecases, showing how a "2-sided polygon" fundamentally represents the circle’s diameter, accountingfor 31.83% of its circumference