A person writing down the numerical value of pi on a blackboard

Pi (π), the 16th letter of the Greek alphabet, is used to represent the most widely known mathematical constant. It is an irrational number, which means that it is a real number with nonrepeating decimal expansion. It cannot be represented by an integer ratio and goes on forever, otherwise known as an infinite decimal.

Indians were the first to observe that the perimeter (circumference) of a circle increases in proportion to its diameter. Therefore, our ancestors established the relation – perimeter/diameter = constant. Regardless of the circle’s size, this ratio will always equal Pi. They didn’t call it “Pi” though. Since the Indus Valley script is not deciphered, it will be incorrect to claim that π was known in the subcontinent in 3000 BC.

However, Indians knew the value of Pi by the time Rigveda was written. The Vedangas and Sulabasutras mention the value of π. The oldest of them, the Baudhayayana Sulabasutra claims that the perimeter of a pit is 3 times its diameter- therefore approximating the value of π at 3. Many other texts, including the Mahabharata and many Puranas approximate Pi at the value of 3.

The constant π helps us understand our universe with greater clarity. In fact, the definition of Pi inspired a new notion of the measurement of angles. This important angle measure is known as “radian measure”, and it gave rise to many important insights into our physical world.

Pi’s ubiquity goes beyond math. The number crops up in the natural world, too. Pi appears everywhere there’s a circle, such as the disk of the sun, the spiral of the DNA double helix, the pupil of the eye, the concentric rings that travel outward from splashes in ponds. Pi also appears in the physics that describe waves, such as ripples of light and sound. It even enters into the equation that defines how we can precisely know the state of the universe, known as Heisenberg’s uncertainty principle.

Finally, Pi emerges in the shapes of rivers. A river’s windiness is determined by its “meandering ratio,” or the ratio of the river’s actual length to the distance from its source to its mouth as the crow flies. Rivers that flow straight from source to mouth have small meandering ratios. It turns out, the average meandering ratio of rivers approaches Pi.

Pi has even trickled into the literary world. Pilish is a dialect of English in which the numbers of letters in successive words follow the digits of Pi. Here’s an example from “Not A Wake,” by Mike Keith, the first book ever written completely in Pilish.

Fun Fact

Pi Day is celebrated on March 14th, to pay tribute to the most famous constant in math and physics.