What you need to know about pi (the number, not the kind we eat)

If you’ve been using Pi Day as an excuse to indulge in some pie, we won’t judge. But there’s a lot more to pi than being a sweet treat. Neil Calkin, a professor in the Clemson University School of Mathematical and Statistical Sciences, tells us why pi matters and why we celebrate the never-ending number on March 14.

What is pi?

Pi is the ratio of the circumference of a circle to the diameter of the same circle. Circumference is the perimeter of a circle, and diameter is the measure from one side of the circle to the opposite side. This ratio is constant; however large or small the circle, pi remains fixed. 

What is pi used for in real life, and why is it important?

You will most likely run into pi when using geometry, and geometry is necessary for architecture, engineering, going to the moon and so much more. 

How many digits of pi do we really need to know?

Pi is an irrational number, which means it has an infinite number of digits and doesn’t repeat. But how many of the digits we need to know depends on the application. NASA or the GPS (global positioning system) on your cell phone doesn’t need more than 15 or 16 digits. If you wanted to measure the diameter of the known universe to within the radius of a hydrogen atom, 28 digits is about what you’d need. “So, you don’t really need very many digits to Pi at all, for any practical reason,” Calkin said.

Has pi contributed to discoveries or inventions?

Sometimes software developers compute pi to test software because this application often reveals issues in new technologies. In the ’90s, a computer chip had a flaw that was discovered when a mathematician noticed incorrect numbers when conducting number theory computations using the chip. The mathematician told the computer company, and it fixed the bug. 

How do you use pi in your research and/or teaching classes? 

I use it in my differential equations class, which focuses on relating a particular function to its derivatives. Exponential and trigonometry functions are essential for studying differential equations, and pi is necessary to understand graphing and patterns of exponential and trigonometry functions. Studying differential equations is necessary for many types of science, like physics and population genetics.

What is your favorite pie?

Steak and kidney pie.

Why can we not identify all the digits of pi?

For most computable numbers, mathematicians can’t calculate all their digits. Specific numbers, like fractions with a whole number in the numerator and the denominator, have repeated patterns. Pi has a pattern when expressed in a form called a nonstandard continued fraction. “We cannot write down the decimal expansion of pi because it’s tough to write down the decimal expansion of anything that is not a rational number,” Calkin said. 

Why did we choose the Greek letter symbol to represent the number pi?

A Welsh mathematician, William Jones, started using π, and Leonard Euler later popularized the symbol. The symbol came from the word periphery in the Greek alphabet. Euler first started using π in 1727 to mean two times the values we know π to tell today, then in 1736, he started using π as 3.14.

What are some of your favorite fun facts about pi?

While in secondary school, teachers usually teach students that an approximation for pi is 22/7, but this approximation is greater than pi. The first four digits of pi are 3.141, while the first four digits of 22/7 are 3.142. Due to misguided approximations like this, the state of Indiana made the “Indiana Pi Bill,” where its legislature came close to declaring that pi was equal to 3.2.  Also, before the symbol π was used, Archimedes approximated the value of pi by inscribing shapes inside a circle. 

Where can I find out more about pi?

Calkin and Eliza Gallagher, an associate professor in the Clemson School of Mathematical and Statistical Sciences, recently published an article on pi in Recreational Mathematics Magazine called “No π For You!”