Question

4) Suppose that Archimedes was feeling very lazy the day he approximated the value of π. Instead of inscribing and circumscribing a circle with regular polygons of 96 sides, he decided to just use squares. What values would he have come up with for an upper bound and lower bound for π if all he used were squares?(Hint: When evaluating the length of the sides of a square inscribed in a circle of radius r, consider drawing a radial line from the center of the circle to one of the corners of the square and then using the Pythagorean Theorem.)

Answer 1