This worksheet demonstrates the use of Maple to show how to approximate the ratio between the perimeter and the diameter of a circle. Since the 18th century this ratio has been known as Pi, and since 1882 it had been known to be a transcendent number. This is an irrational number, which satisfies no algebraic equation but can be calculated, by means of infinite series, to any desired number of decimal places. Using computers, Pi has been calculated to over 200,000,000,000 digits. In this worksheet, the author uses Maple to implement Archimedes’s method for calculating Pi.