How Pi Works

By: Marshall Brain & Dave Roos  | 
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.


National Pi Day

model in pi sweater
This model is ready to celebrate Pi Day, as he walks the runway at the Niyazi Erdogan show during Mercedes Benz Fashion Week in Istanbul, Turkey, 2015.
Andreas Rentz/Getty Images For IMG

National Pi Day was officially recognized by the United States Congress in 2009, but the (definitely not "square") roots of the holiday can be traced back to 1988 and a man named Larry "The Prince of π" Shaw [source: Exploratorium]

Shaw was a beloved longtime employee at the Exploratorium, a science museum in San Francisco, California, and came up with the idea of "π Day" on a 1988 staff retreat following the death of Exploratorium founder Frank Oppenheimer. It was almost too perfect: The first digits of Pi are 3.14 — March 14!


Even better, March 14 is also Albert Einstein's birthday, making π Day the ultimate geeky double-header.

The first π Day celebration was nothing more than Shaw and his wife handing out slices of fruit pie and tea at 1:59 PM (the three digits following 3.14), but the holiday quickly gained fame in the Bay Area.

Shaw eventually built the "Pi Shrine" at the Exploratorium, a circular classroom with a circular brass plaque at its center. Every Pi Day celebration at the Exploratorium ended with a colorful parade led by Shaw blasting his boombox (with a remix of "Pomp and Circumstance" set to the digits of pi) and circling the Pi Shrine exactly 3.14 times. The parade ended with the singing of "Happy Birthday" to Albert Einstein.

The Prince of π passed away in 2017, but the annual Exploratorium party continues, as do π Day celebrations the world over. Popular ways to celebrate include baking a pie and other circular treats; making a construction paper pi chain, where each 10 digits is a different color; and creating a collage out of circular shapes [source: National Pi Day].

You can also challenge your friends to a pi memorization contest. For a little context, the current world record for memorizing and reciting the most digits of pi was set by Suresh Kumar Sharma of India in 2015 when he recited a staggering 70,030 digits in 17 hours and 14 minutes. Why don't you start with 20?


Originally Published: Mar 13, 2019

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More Great Links

  • Exploratorium. "A Brief History of Pi (π)" (March 8, 2019)
  • Exploratorium. "A Slice of Pi (π) Day History" (March 8, 2019)
  • NASA Jet Propulsion Laboratory. "How Many Decimals of Pi Do We Really Need?" March 16, 2016. (March 8, 2019)
  • Pi World Ranking List. "Pi World Ranking List" (March 8, 2019)
  • Roberts, Gareth Ffowc. "Pi Day 2015: Meet the Man Who Invented Pi." The Guardian. March 14, 2015 (March 8, 2019)