Why Pi Is So Popular on Pi Day

Every year on 14 March, numerophiles and mathematicians traditionally take a moment to consider pi, the best-known of all irrational numbers.

Pronounced pie, represented by π, and commonly abbreviated to 3.14, this apparently straightforward number has become a symbol of how useful, lyrical and far-reaching mathematics can be in the modern world.

But why is pi the number that receives the celebration rather than e or the golden ratio? And should tau day be given greater attention instead?

Not everyone believes pi merits all this admiration. Even so, it remains undeniably charming.

What is pi?

Pi (π) is the constant that expresses the relationship between a circle’s circumference and its diameter. As an irrational number, it is generally rounded to two decimal places: 3.14.

Interested in all the remaining digits? Since they continue forever, writing them down would take some time. However, the first 200 decimal places are available in song form. Have a go at singing them!

The Greek letter P was selected in the 18th century by Welsh mathematics teacher William Jones, probably because it referred to ‘periphery’.

The symbol pi was intended to represent more than an ordinary number. Before it came into use in the early 18th century, this quantity had been denoted through words and fractions, neither of which properly conveyed an unfathomable and endless string of non-repeating decimal digits.

Jones may have believed that "'the exact proportion between the diameter and the circumference can never be expressed in numbers", although Swiss polymath Johann Lambert did not prove pi’s irrationality until the 1760s.

When was pi first calculated?

It appears that people have recognised for as long as they have studied circles that a circumference measures roughly three diameters, irrespective of the circle’s size.

Evidence for this relationship can even be found in Babylonian mathematics from about 4,000 years ago. The Babylonians knew that the perimeter of a hexagon fitting neatly within a circle equalled six times the radius, producing a value of 3.125.

The Rhind Papyrus (below), created in Ancient Egypt around 1650 BCE, stated that if you removed "1/9 of a diameter and construct a square upon the remainder; this has the same area as the circle", giving a value of 3.16049.

(British Museum Department of Ancient Egypt and Sudan/PD)

Archimedes of Syracuse also made a strong attempt to solve the question. Like the Babylonians, he used polygons and multiplied their sides, arriving at a more theoretical estimate between 3 and 1/7, and 3 and 10/71.

Why is pi so popular?

Because pi is constant for every circle, it is an axiom - a fundamental principle - that helps explain a wide variety of concepts and phenomena across geometry and physics.

It is therefore valuable for an enormous range of uses in describing and analysing the natural world, from winding rivers to the structure of atoms.

Pi can also turn up unexpectedly where circles seem to have no obvious role. For instance, the probability that two integers share no positive common factors - meaning they are relatively prime - equals 6/π^2.

In addition to its mathematical and practical value, pi has fascinated the public for poetic and aesthetic reasons alone. At a staff retreat in 1988, Larry Shaw, a physicist and staff member at San Francisco’s Exploratorium, noticed that 14 March mirrored pi’s opening three digits, 3.14.

That observation gave rise to Pi Day, a celebration of science and mathematics. More than three decades later, it is observed worldwide through pi facts, mathematical challenges and baking the best-known circular dessert: pie.

(ScienceAlert)

This article is adapted from a previously published ScienceAlert Explainer article.