Sebastian Cioaba, professor in the Department of Mathematical Sciences, explains how the Greek mathematician Archimedes calculated an accurate estimation of pi.

# Celebrating Pi Day

Photo by Kathy F. Atkinson

## UD math professor Sebastian Cioaba shares insights about pi

Divide the circumference of a baseball by its diameter and you get 3.14. Divide the circumference of Earth by its diameter and you get 3.14. Divide the circumference of a pizza, coin or, well, pie and — you get the point.

The definition of pi is fairly simple: It's the ratio of the circumference of any circle to the diameter of that circle.

In celebration of the most famous mathematical constant, people eat pie and memorize digits on Pi Day — Tuesday, March 14, or 3/14 as it's written in many countries. Pi Day was started in 1988 by Larry Shaw, a physicist who worked at a San Francisco museum. It wasn’t until 2009, however, that it became an official national holiday in the United States. In 2019, the United Nations Educational, Scientific and Cultural Organization (UNESCO) proclaimed March 14 as the International Day of Mathematics.

Regardless of a circle's size, the ratio will always equal approximately 3.14159. Pi is an irrational number, meaning that its decimal form neither ends (like 3/4 = 0.75) nor becomes repetitive (like 1/3 = 0.333333...). Mathematicians began using the Greek letter for p — or π — in the 1700s. It was introduced by English mathematician William Jones in 1706, and use of the symbol was popularized by Swiss mathematician Leonhard Euler, who adopted it in 1737.

“The interesting thing about pi is that it pops up in all kinds of places,” said Sebastian Cioaba, professor in the Department of Mathematical Sciences at University of Delaware. “Students, and people in general, think that the mathematics landscape consists of separate islands that aren’t connected, and that's the opposite. Circles are ubiquitous in mathematics, so whenever there's a circle, pi will be involved.”

Pi shows up everywhere in mathematics and science in places and forms where one expects to see it, such as calculus in the form of infinite sums, products or integrals. But it also appears in places one less expects to encounter it, such as number theory, probability or combinatorics, said Cioaba, who discusses pi in his recent book, A Bridge to Advanced Mathematics: From Natural to Complex Numbers.

“I think any attention to math is great,” Cioaba said. “When people think about pi, the fixation is so much on the digits — how many you can memorize. That’s fine, and it gets kids interested in it. But I don't find that's the most interesting thing about pi.”

Greek mathematician Archimedes is credited as one of the first people to calculate an accurate estimation of pi’s value, sometime around 250 BC. He determined the length of the perimeter of a polygon inscribed within a circle (which is less than the circumference of the circle) and the perimeter of a polygon circumscribed outside a circle (which is greater than the circumference). The value of pi is between those two lengths.

Archimedes began by inscribing an equilateral triangle inside of a circle. By doubling the number of sides of the triangle to a hexagon, then a dodecagon, then a 24-sided polygon, and finally 48- and 96-sided polygons (and then repeating that process on the outside of the circle), he was able to determine that pi was less than 3 1/7 but greater than 3 10/71.

“The hexagon approximates your circle better than the triangle — it gets closer to it — and then you go to the dodecagon with 12 sides, but still, it's not perfect. And then you continue,” Cioaba said. “The way the Greeks saw the circle is this kind of pinnacle or culmination of polygons. The idea is polygons becoming circles, but they never become circles. It’s kind of like this lofty dream — they try to become circles, but they never become circles. But it helps with getting to pi.”

Cioaba grew up in Romania and had never heard of Pi Day until he came to Canada as a graduate student. Indeed, pi is pronounced differently in Romania, and “there’s no relation between the food and the number.”

But as a professor, he saw that students were excited about the day — and therefore the number — and anything that gets students excited about math is something he embraces. Likewise, Cioaba said he appreciated his department colleagues, including the late Pam Irwin — yes, PI — for their enthusiasm in helping students.

“I liked math because I had really good teachers,” Cioaba said. “It was a combination of various teaching methods that made me like it. Once I got curious, I really liked it, and I wanted to learn on my own as well. A lot of people have the opposite experience — they had an open mind and then something happened that kind of shut the door in their face, and then they don't have the confidence to open it by themselves. They need help to open it, and that's what we have to provide to young people. So whatever we do — you know, Pi Day, whatever — I'm all for it if it gets people excited about math.”

Math can have a bad reputation, Cioaba said, but leaning into that curiosity is critical. He encourages students to memorize the first 10 or even 20 digits of pi because that might give them the confidence to learn more.

“That's the thing about math — it’s all about connections,” he said. “Do your homework, and don’t be afraid to ask questions. A student should be willing to accept that they don't know things — that's why you're in school. It’s okay to not know everything. I don't know everything. I make mistakes. It's okay to make mistakes, as long as you keep learning and as long as you keep trying.”

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