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Archaeology Odyssey 3:2, March/April 2000

# Origins: 3.14159265…

Why did the ancients invent increasingly subtle and ingenious methods to arrive at an exact value of p? Human curiosity.

Archaeology Odyssey

How do you find the holy grail of mathematics?

You start with a circle, which is the easiest geometric shape to draw (just fix one end of a string in place and swing the other end around it, inscribing a circle). Then measure the circle’s perimeter (also known as the circumference) and the distance across its widest point (the diameter). Divide the circumference by the diameter—and you have that well-known but eternally daunting number, p, or pi, which has a value of 3.14159265…

That is part of the mystique of p: Whatever the size of the circle, the value remains the same (what mathematicians call a “constant”). Unfortunately, p is also “irrational,” meaning that it is impossible to calculate its value completely; the decimals go on forever without regular repetition.

Calculating the value of p has been a puzzle for millennia. One of the earliest implied values is given in a biblical passage describing the construction of a huge basin for Solomon’s Temple: “Then [Hiram of Tyre] made the molten sea; it was round, ten cubits from brim to brim, and five cubits high. A line of thirty cubits would encircle it completely” (I Kings 7:23). In other words, p = 30÷10 or 3.