Archimedes and the Enigmatic Ratio of Pi (π)

Mark Rademaker, The Netherlands, Assen

Pi (π) is an irrational number. This means it cannot be expressed as a common fraction. Also, π is a transcendental number; that is, it is not the root of any polynomial having rational coefficients. This transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. For all of you that understand all of that, I am extremely impressed. I am also extremely impressed that the famous mathematical ratio of a circle’s circumference to its diameter is estimated to more than 22 trillion digits (and counting!) The Greek geometer Archimedes, some 2,300 years ago, first showed how to estimate the value of pi by using a large number of tiny straight lines or flat polygons. I understand the theory of pi and marvel at the infinite uses in our everyday lives from reconstructive facial surgery to computer-generated movies. I also love the human ingenuity that saw fit to celebrate infinity with good, old-fashioned, edible, pie—also circular, baked and containing either sweet or savory ingredients. So, as we prepare to celebrate 3.14, also known as March 14, by eating pie mathematically defined by pi, I am struck by the irony of Archimedes’ mathematical genius. “To Infinity and Beyond” indeed.