What methods/calculations were used to calculate the value of $\pi$ ($3.14\ldots$). Was it simply determined by calculating the circumference of a circle then dividing by the diameter, or some other method?
2026-03-27 03:45:04.1774583104
How did $\pi$ originate?
339 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
In around 250 BC, Archimedes expressed $\pi$ as a limit. He constructed sequences of inscribed and circumscribed polygons whose perimeters were lower and upper bounds of the value of $\pi$ respectively, such that the perimeters converged to the same value.
I do not know how rigorously the ancient Greeks were capable of proving that the perimeters truly were upper and lower bounds on $\pi$, that the difference in the perimeters converged to zero, and that the limits existed.
They did understand the squeeze theorem (by the name of the "method of exhaustion), however, so they did understand in their own way that this construction expressed $\pi$ as a limit.
Reference: wikipedia