Pi Before Pi

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Wikimedia Commons

Although our ancestors had managed to invent the wheel millennia prior to the good ol’ days of Ancient Egypt, it wasn't until that civilization arose thousands of years later that the human race began to understand the mysteries behind the circle. Our modern comprehension of pi, or the ratio of a circle’s circumference to its diameter, is a fairly recent development in our history, and the Egyptians were the first on the ball.

The Rhind Mathematical Papyrus (above), excavated in the area surrounding the Memorial Temple of Pharaoh Rameses II in Egypt, constitutes the finest example of ancient Egyptian mathematics, as well as their claim to having discovered pi. Its author, Ahmose, titled the work “Directions for Attaining Knowledge of All Dark Things,” but its contents were much less sinister than its name suggested. Of the 87 problems into which the content of the papyrus was divided, the 48th and 50th were those which suggested genuine insight into things previously unknown. 

Problem 48 of the RMP showed a circle inscribed within a square, with hieroglyphic markings denoting its value as 64; problem 50 followed up on this information with a procedure to find “the area of a round field with a diameter of 9 khet.” The steps given call for subtracting 1/9th of the circle’s diameter, leaving 8, then multiplying it by 8, for an area of 64. After some substitution using our contemporary knowledge of the circle area formula as π * r2, the Egyptians seem to have calculated the constant value of pi as 256/81, or 3.16—not bad for a first attempt in 2000 BC.

As human civilization, and consequently the field of mathematics, advanced, great minds of every age tackled the question of pi. In 250 BC, Archimedes calculated the areas of a polygon inscribed within a circle and the polygon in which that same circle was inscribed, knowing that pi must lie between the two, and determined its exact value must be between 3 1/7 and 3 10/71. Chinese astronomer Zu Chongzhi, independently of Archimedes’s findings and approximately 700 years later, carried out a series of painstaking calculations on 24,576-sided polygon to approximate pi as 355/113.

In the early days of computer technology, new machines were put to the test by calculating pi: the amount of its digits that the computer could process served as an easy benchmark for its overall computing power. As technology has improved exponentially in the past few decades, so too has our knowledge of pi: as of September 2010, we know 2,000,000,000,000,000 digits of pi—that’s two quadrillion digits. According to Nicholas Sze, the Yahoo! engineer who used 1000 of the company’s computers and its Hadoop cloud computing app to calculate pi over a period of 23 days, that final (for now) digit is 0.

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March 15, 2013 - 8:00am
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