Every March 14 (3/14), mathematicians, scientists and math lovers around the world celebrate Pi Day, a commemoration of the mathematical sign pi (π), expressed most simply by the decimals 3.14 (although they go on *forever*, of course; more on that later).

Weihong Guo, Chair of the Department of Mathematics, Applied Mathematics and Statistics at Case Western Reserve University, said the number, while perhaps somewhat mysterious to the more math-challenged among us, is actually “the most useful number human beings have….”

But what does pi mean? What does it do? Why does it do it? *The Daily *sat down with Guo to learn more.

## Pi defined

In short, pi is *the ratio of the circumference of any circle to the diameter of that circle*.

So, no matter how big a circle is—the top of a soda can or the cross section of donut—the ratio of its circumference (the distance around the circle) to its diameter (a line straight across its middle) will always equal pi—approximated as 3.14 in decimal form.

Or: 3.14159265358979323846, if you care to go out 20 decimal places. But, again, it never ends and never repeats.

“A lot of people know pi through their geometry classes in school, but that’s really it—they’re not sure why it’s important,” Guo said. “In reality, pi is really the most useful number human beings have to use for so many things in the real world.”

Those real-world examples range from calculating the surface area of a soda can (“How much material do you need to make this thing? Make a million of them?” Guo said) to sizing age-appropriate soccer balls to using a “Gaussian density,” the familiar bell-shaped curve that plays a central role in statistics and probability.

Guo said pi also “gave rise to many important insights in our physical world. It’s been used to help calculate the orbit of planets in the solar system and examine how ripples in rivers carry energy.”

## Pieces of pi

Pi is an irrational number—a number that sits in the limitless space between whole numbers “3” and “4.”

“We all learned the natural numbers like 1, 2, 3 from the time we are toddlers to do counting,” Guo said, “but those numbers don’t cover all of the *actual *numbers from negative infinity to positive infinity. More advanced ideas need more advanced math that requires more advanced numbers and there are an infinite number of irrational numbers. Pi is one of them.”

Some other pieces of pi:

- The first calculation of π was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world.
- Check out this “Song from Pi.” It says it all.
- The first official Pi Day was held in 1988 at at San Francisco’s science museum Exploratorium.

Guo’s other research interests include mathematical image analysis and processing, inverse problems, scientific computing and computer vision.