(From Wikipedia) The first recorded algorithm for rigorously calculating the value of π was a geometrical approach using polygons, devised around 250 BC by the Greek mathematician Archimedes, implementing the method of exhaustion. This polygonal algorithm dominated for over 1,000 years, and as a result π is sometimes referred to as Archimedes's constant. Archimedes computed upper and lower bounds of π by drawing a regular hexagon inside and outside a circle, and successively doubling the number of sides until he reached a 96-sided regular polygon. By calculating the perimeters of these polygons, he proved that 3.1408 < π < 3.1429.
I thought pi is a really mysterious value, with its infinite decimal expansion and its significance in geometry, physics, and many other fields. I once heard about a method to approximate the value of pi by continually increasing the number of sides of a polygon inscribed within a circle. This method intrigued me greatly, prompting me to wonder whether I could utilize optimization techniques or my coding skills to tackle this problem.
My project for exploring pi approximations can be accessed at this link.