Pi (often represented by the lower-case Greek letter π), one of the most well-known mathematical constants, is the ratio of a circle’s circumference to its diameter. For any circle, the distance around the edge is a little more than three times the distance across. Typing π into a calculator and pressing ENTER will yield the result 3.141592654, not because this value is exact, but because a calculator’s display is often limited to 10 digits.

Pi is actually an irrational number (a decimal with no end and no repeating pattern) that is most often approximated with the decimal 3.14. π is commonly defined as the ratio of a circle’s circumference C to its diameter d.

Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number piWilliam L. Schaaf,Nature and History of Pi

Pi has interested people around the world for over 4,000 years. Many mathematicians – from famous ones such as Fibonacci, Newton, Leibniz, and Gauss, to lesser well-known mathematical minds – have toiled over pi, calculated its digits, and applied it in numerous areas of mathematics. Some spent the better parts of their lives calculating just a few digits.

Around 250 BC, the Greek mathematician Archimedes** ^{[1]}** created an algorithm to approximate π with arbitrary accuracy. In the 5th century AD, Chinese mathematicians approximated π to seven digits, while Indian mathematicians made a five-digit approximation, both using geometrical techniques. The first computational formula for π, based on infinite series, was discovered a millennium later. The earliest known use of the Greek letter π to represent the ratio of a circle’s circumference to its diameter was by the Welsh mathematician William Jones

**in 1706.**

^{[2]}There is an entire language made from the number Pi. But how is that possible? Well, some people loved pi enough to invent a dialect based on it. In “Pi-lish” the number of letters in each word match the corresponding digit of pi. This first word has three letters, the second has one letter, the third has four letters, and so on. This language is more popular than you might think. Software engineer Michael Keith wrote an entire book, called *Not a Wake* in this language.

Tau, the 19th letter of the Greek alphabet, is the ratio of the circumference to the radius of a circle, which is equal to 2π (6.28318…). Some believe that tau is better suited to circle calculations. For instance, you can multiply tau with the radius of a to calculate its circumference more intuitively. Tau/4 also represents the angle of a quarter of a circle.

In the Exploratorium science museum, a circular parade happens every year on pi day. Each person participating holds one digit in the number pi. It wasn’t celebrated around the United States like it is now until Congress passed Resolution 224, which designated March 14th as pi day.

Congress hoped that celebrating pi day would cultivate a higher level of enthusiasm for math and science among American students. Givenchy sells a men’s cologne with the name ‘Pi’. The company markets this product as capable of enhancing the attractiveness of intelligent and visionary men.

While we know pi to more than a trillion places, we really don’t need them. Scientists can determine the spherical volume of the entire universe using just 39 places past the decimal. NASA’s Jet Propulsion Laboratory only uses pi up to 15 decimal places for its robotic space and earth science missions.

For JPL’s highest accuracy calculations, which are for interplanetary navigation, we use 3.141592653589793. There are no physically realistic calculations scientists ever perform that would require more decimal points than that.

Marc Rayman– JPL Engineer

People have found math books from before 1706 that refer to the number as a lengthy Latin phrase that translates to “the quantity which, when the diameter is multiplied by it, yields the circumference.” A British mathematician named William Jones was the first person to call the quantity π, in 1706. In 2014, 589 people at a grammar school in Germany formed the largest human pi symbol.

And in 2017, 520 teachers and students in Todi, Italy, formed the longest human representation of pi digits. Pi: Finding Faith in Chaos is the 1998 film, which won an Independent Spirit Award for screenwriter Darren Aronofsky, is admittedly a bit of a downer, as it follows a tormented mathematician trying (and failing) to work out the secrets of the universe. In the Sandra Bullock thriller The Net, clicking on a pi symbol is what sends Bullock’s character into the confidential government files,

and in Alfred Hitchcock’s Torn Curtain, the pi symbol is the code that represents the escape network. It’s even vanquished TV villains; in a Star Trek episode, Spock outsmarts an evil computer by challenging it to calculate the final digit of pi.

##### Footnotes

- Archimedes of Syracuse (c. 287 – c. 212 BC) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Considered the greatest mathematician of ancient history, and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems. These include the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral. Archimedes’ other mathematical achievements include deriving an approximation of pi, defining and investigating the Archimedean spiral, and devising a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, working on statics and hydrostatics. Archimedes’ achievements in this area include proof of the law of the lever, the widespread use of the concept of center of gravity, and the enunciation of the law of buoyancy or Archimedes’ principle. He is also credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion. [Back]
- William Jones, (1675 – July 1, 1749) was a Welsh mathematician, most noted for his use of the symbol π (the Greek letter Pi) to represent the ratio of the circumference of a circle to its diameter. He was a close friend of Sir Isaac Newton and Sir Edmund Halley. In November 1711 he became a Fellow of the Royal Society and was later its vice president. [Back]

##### Further Reading

##### Sources

Pi Day

Wikipedia

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