Pi Facts – What Is the Number Pi?

Pi is an irrational number.
Pi is the ratio of a circle’s circumference to its diameter.

The number π or pi is a mathematical constant that is the ratio of a circle’s circumference to its diameter (π = C/d). The ratio is a constant no matter what size of circle is used. Pi is also called Archimedes’ constant. Although pi is often approximated as 3.14159, its true value consists of an infinite number of digits that never settle into a repeating pattern. In other words, it is an irrational number. Here is a collection of interesting and intriguing pi facts, including some most people don’t know:

Funny, Strange, and Interesting Pi Facts

Squaring the circle is impossible because pi is a transcendental number.
  • Because it relates to the circle, the most common places to encounter pi are in geometry, trigonometry, number theory, and physics.
  • Pi gets its name from the Greek letter π, which is the first letter in the Greek word perimetros, which means circumference. The symbol for the constant was introduced by Anglo-Welsh philologist (person who studies languages) and mathematician William Jones in 1706.
  • Because pi is often rounded to 3.14, Pi Day is celebrated March 14th. Pi Day got started by physicist Larry Shaw at San Francisco’s Exploratorium museum. On Pi Day, the Exploratorium holds a circular parade in which each person holds a card for a digit of the number. Pi Day is a good day to find deals on pie and pizzas!
  • Albert Einstein’s birthday is Pi Day. He was born March 14, 1879. Stephen Hawking died on Pi Day. He died March 15, 2018.
  • Because pi is an irrational number, it can only be approximated by fractions. Fractions used to approximate pi (from least to most accurate) are 22/7, 333/106, and 355/113.
  • In addition to being irrational, pi is also a transcendental number. This means it is not the solution to any non-constant polynomial equation with rational coefficients. While the definition of “transcendental” may be confusing to any non-mathematician, the consequences are easier to understand. First, pi can’t be written using any combination or square roots or rational numbers. Second, it can’t be constructed using a compass and straightedge. In other words, it is impossible to “square the circle” by using a compass and straightedge to make a square with an area exactly equal to that of a circle.
  • The ancient Egyptians and Babylonians knew about pi and tried to compute it. Archimedes wrote an algorithm to calculate it around 250 BC, while Indian and Chinese mathematicians used geometry to make five-digit and seven-digit approximations (respectively) in the 5th century AD. The first exact formula came in the 14th century from the Madhava-Leibniz infinite series.
  • The memorization of the digits of pi is named piphilology. Despite its “ology” ending, it isn’t a science, but it is a great memory test! The Guinness World Record for the feat is 70,000 digits, as recited by Rajveer Meena in 9 hours and 27 minutes in March of 2015. Akira Haraguchi is said to have recited pi to 100,000 decimal places, but his claim was not verified for the world record.
  • One way to memorize pi digits is to write a poem called a piem. A piem consists of words with lengths that represent the digits. The first word has three letter, the second letter has one letter, and so on. An example of a piem is one written by English scientist James Jeans: “How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics.”
  • The digits of pi have been used as a language in a form of constrained writing. The word lengths represent digits of pi. The book Not a Wake contains 10,000 words, each representing a pi digit.
  • In 1897, the Indiana legislature was presented with the Indiana Pi Bill, which would have changed the value of pi to 3.2 and required states besides Indiana to pay a royalty to use the new number. Dr. Edward Goodwin of Indiana believed (incorrectly) he had solved the problem of “squaring the circle.” The Indiana State House of Representative passed the bill 67-0, but Purdue University professor Clarence Waldo heard the bill debate on the radio. He educated the state’s senators about geometry and the Senate killed the bill.
  • Some mathematicians want pi to be replaced by tau (τ). The problem is that tau isn’t defined the same way by everyone. Albert Eagle proposed using tau in 1958, defining it as π/2. He reasoned this would make formulas simpler. However, many people define tau as 2π or approximately 6.28. If Tau Day replaced Pi Day, it would be celebrated on June 28th, presumably by eating double portions of pizza or pie!
  • The Massachusetts Institute of Technology (MIT) used to mail application decision letters so students might receive them on Pi Day. In 2012, MIT posted decision online on Pi Day at 6:28 pm (“Tau Time”). In 2015, decisions were posted at 9:26 am, which was the “pi minute.”

References and Further Reading

  • Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4.
  • Beckmann, Peter (1989). History of Pi. St. Martin’s Press. ISBN 978-0-88029-418-8.
  • Blatner, David (1999). The Joy of Pi. Walker & Company. ISBN 978-0-8027-7562-7.
  • Hallerberg, Arthur (May 1977). “Indiana’s squared circle”. Mathematics Magazine. 50 (3): 136–140. doi:10.2307/2689499
  • Schepler, H.C. (1950). “The Chronology of Pi”. Mathematics Magazine. 23 (3): 165–170 (Jan/Feb), 216–228 (Mar/Apr), and 279–283 (May/Jun). doi:10.2307/3029284