Measurement of the Circle

Archimedes' work, Measurement of the Circle, established bounds for the mathematical constant pi. He demonstrated that pi is between 3 10/71 and 3 1/7. Archimedes used the method of exhaustion to approximate the area of a circle by inscribing and circumscribing polygons with an increasing number of sides. This method allowed him to determine upper and lower bounds for pi, showing that its value lies between these two fractions. He also proved that the area of a circle is equivalent to the area of a triangle with a height equal to the circle's radius and a base equal to its circumference.12