In 2009, the United States Congress officially declared March 14 as National Pi Day. The day is meant to celebrate all things 3.14, the approximate value of Pi.

We asked Dr. Carlos Ortiz, a professor in the Mathematics and Computer Science Department, to shed some light on pi, something we’ve probably all heard about but may not know much about.

Why is pi so important in mathematics?
Pi is one of these magical numbers that appears very early on in many different civilizations such as the Egyptians, Chinese, and Greeks. The reason? It was present in every geometrical consideration of a circle, which is a geometric figure that is everywhere in our daily experience.  

Everywhere on the planet, people noticed that if you divided the perimeter of a circle by its diameter, you always got the same number. They called such a magical number pi.

So the number pi seems to be a feature of this “flat” universe. It appears everywhere there are circles. To add to the mystery, when trying to calculate pi exactly, people noticed that pi has an infinite decimal expansion, and that this expansion does not repeat itself. In modern terms, we say that pi is irrational. This means that we cannot know pi exactly. This seemed to many people to endow pi with mystical qualities: it never ends, we cannot predict its values, and it goes on forever, capturing infinity in it.

Then, it turned out that because pi is so closely tied to circles, many important geometric formulas for calculating areas and volumes of circular and spherical objects involved pi. Also, pi is essential to calculate distances from angles, a discipline known as trigonometry.

Can you give us some real-world examples of how pi is used?
Knowledge of pi is essential for many things. A couple of examples include the manufacturing and design of circular objects such as gears, wheels, and bearings, and for accurately computing dimensions, tolerances, and amounts of materials.

A precise knowledge of pi is also essential for navigation on Earth and in astronomy, for example for calculating distances on spherical bodies, like our planet.

We hear of people trying to memorize hundreds of digits of pi. Do you think that has any real mathematical benefit, or is it just for fun?
In most scientific or engineering calculations, it is enough to know pi up to a limited number of digits. The world record for calculating the digits of pi is around 105 trillion digits, which was found using computing resources.

Because of this, memorizing the digits of pi has no mathematical utility, but it has great utility to improve memory and mental discipline of individuals performing such a feat.