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Sebastian Cioaba, professor in the Department of Mathematical
Sciences, explains how the Greek mathematician Archimedes calculated an
accurate estimation of pi.
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
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
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
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
“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
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
“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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Article by Amy Wolf, photo by Kathy F. Atkinson
Published March 13, 2023