I read recently that two supercomputer manufacturers were in a contest to determine who could calculate pi to the most digits. My simple question, simple for you at least, is, what data do they input to begin these calculations? Every schoolchild knows that pi is the ratio of a circle’s circumference to its diameter. Obviously mathematicians do not draw a circle and then measure out the circumference with increasingly tiny rulers. But what do they do instead? –Maxwell Stephens, Washington, D.C.
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Dreaming up “algorithms” (techie talk for “methods”) to compute pi has occupied the world’s great minds for more than two millennia. Clearly these aren’t guys you’d want to go on a long fishing trip with. The ancient Greeks used a simple method: You draw polygons (e.g., hexagons) around a circle with a diameter of one–one inside, one out. Calculate the perimeter of the polygons (which is pretty straightforward), take an average, and you get a rough idea of pi. Use polygons with more sides and your approximation of pi gets closer and closer. The mathematician Archimedes got as far as 96 sides, calculating that pi was between 3.1408 and 3.1428.
Why compute one billion digits? God knows. As one learned treatise notes, “thirty-nine places of pi suffice for computing the circumference of a circle girdling the known universe with an error no greater than the radius of a hydrogen atom.” One pi-wars participant rationalizes by saying once you get beyond a billion digits subtle patterns may begin to emerge in the numbers, but give me a break. The real reason, many feel, is “because it’s there.” So immature. Thank God the rest of us have put such foolishness behind us.
Art accompanying story in printed newspaper (not available in this archive): illustration/Slug Signorino.
