How Pi Works

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Pi is an extremely interesting number that is important to all sorts of mathematical calculations. alengo/Getty Images

Pi has mesmerized mathematicians for 4,000 years. It's the rarest of mathematical constants, an unfailingly accurate ratio that's also neverending. The digits of Pi have been calculated out to more than 22 trillion decimal places without ever repeating (that's called an "irrational number").

The definition of pi is simple: It's the ratio of a circle's circumference divided by its diameter. But what's remarkable is that no matter the size of the circle you are measuring, that ratio of circumference to diameter will always equal 3.1415926535897, usually shortened to 3.14. Divide the circumference of a tennis ball by its diameter and you get 3.14. Divide the circumference of the planet Mars by its diameter and you get 3.14. Divide the circumference of the known universe by its diameter — you get the point. As one mathematician put it, "Pi is part of the nature of the circle. If the ratio was different, it wouldn't be a circle."

The following figure shows how the circumference of a circle with a diameter of 1.27 inches (32.35 millimeters) is equal to a linear distance of 4 inches (10.16 centimeters):


As you might imagine, 4.0 (the circumference) / 1.27 (the diameter) = 3.14.

Pi is critical to several basic calculations in geometry, physics and engineering, including the area of a circle (πr2) and the volume of a cylinder (πr2)h. When the ancient Babylonians attempted to measure the precise areas of circles back in 1900 B.C.E., they assigned a value to pi of 3.125. The ancient Egyptians came up with 3.1605. The Greek mathematician Archimedes (287-212 B.C.E.) and the Chinese mathematician Zu Chongzhi (429-501 C.E.) are co-credited with calculating the most accurate approximations of pi before calculus and supercomputers gave us the definitive answer [source: Exploratorium].

In 1706, the self-taught Welsh mathematician William Jones assigned the Greek letter π to this magical number without end, possibly because π is the first letter of the Greek words for periphery and perimeter. The symbol's use was later popularized by 18th-century Swiss mathematician Leonhard Euler but wasn't adopted worldwide until 1934.

The fact that pi can be found everywhere — not only in circles, but in arcs, pendulums and interplanetary navigation — and that it's infinitely long has inspired a cult following that includes plenty of geeky tattoos and even its own national holiday. Keep reading to learn how you, too, can celebrate National Pi Day.