Pi by the numbers

Today is the occasion of two venerated observances in math and science. In the first instance, it is a celebration of Albert Einstein’s birthday. He was born March 14, 1879 — 135 years ago today.

The second noteworthy occasion is National Pi Day. Because today’s date may be expressed as 3/14, mathematicians have taken on the day as 3.14 which is an abbreviated way to express the numerical value of Pi.The number π is a mathematical constant, the ratio of a circle’s circumference to its diameter, approximately equal to 3.14159.

While these two occasions are likely of greatest interest to the horn-rimmed glasses and library types, we can all have a little fun thinking about the things it represents. Of course, Einstein’s contribution to science needs little elaboration. His name is synonymous with great intellect. His work transformed the way we think about the physical universe.

Millennia before Einstein, there was another thinker whose contributions changed the face of the ancient world. The third century BCE Greek mathematician, Archimedes, had a similar gravity in his day. Like Einstein, Archimedes was known for many things. Just as Einstein is associated with the equation e=mc2 so too is Archimedes known for his own computational triumph.

In Proposition Three of his work, Measurement of a Circle, Archimedes states, “The ratio of the circumference of any circle to its diameter is less than 3 1/7 but greater than 3 10/71.”

In short, Archimedes articulated one of the earliest accurate calculations of Pi. As most great scientific discoveries do, Archimedes’ finding stood on the shoulders of another scientific luminary, the Greek mathematician, Euclid.

In his work Elements, Euclid states, “If an angle of a triangle be bisected and the straight line cutting the angle cut the base also, the segments of the base will have the same ratio as the remaining sides of the triangle; and, if the segments of the base have the same ratio as the remaining sides of the triangle, the straight line joined from the vertex to the point of section will bisect the angle of the triangle.”

What Euclid’s telling lacks in brevity, it compensates in instructiveness. Archimedes applied Euclid’s work in a very novel way. Instead of approaching the estimation from a geometrical perspective, he uses a method that is wholly mathematical. As researchers at Florida Gulf Coast University observe, this method, “…probably would have horrified Plato but was actually common practice in Eastern cultures, particularly among the Chinese scholars.”

Again, we see the value of collaborative thinking and respectful appropriation of ideas. This manifests again in the 18th century when the Welsh mathematician, William Jones, first used the Greek Pi character to denote the ratio. This became common after Swiss mathematician Leonhard Euler adopted its use in 1737.

As to the modern observance of Pi day, mathematicians will likely have their own ideas. A common event is a contest to see who can recite from memory the longest string of digits related to the equation. As most know 3.14 are just the first three digits of the ratio. It goes on infinitely with no discernable pattern.

For the rest of us, the occasion is likely best commemorated with a few well-placed puns.

At Princeton University — Einstein’s longtime university home — Pi Day is marked by pie (the pastry) baking and eating. Others note comestibles with the letters p and i in their names like pizza and Pina Coladas. However one chooses to mark the day, we should all pause to think about the importance of a good grounding in math. As the U.S. strives to keep its place among the leading nations of the world, math education is paramount.