What was the method that Archimedes used to estimate the value of pi?

Archimedes estimated the value of pi by inscribing and circumscribing polygons around a circle. He started with a hexagon and progressively doubled the number of sides, calculating the perimeters of these polygons to get upper and lower bounds for the circumference of the circle. By using a 96-sided polygon, he determined that pi was approximately between 3.1408 and 3.1429, providing one of the earliest known estimates of the mathematical constant. This method demonstrated the relationship between the circle's diameter and its circumference through geometric means.