# Pi-Day: sine, sine, cosine, sine, 3.14159!

March 14th is π-day (Pi-day) – a day to celebrate the mathematical constant π, which is commonly approximated as 3.14.

For some irrational reason, someone, somewhere decided that π was worthy of an annual celebration, and of course, the only rational choice was the 3rd month and 14th day of the year. I get the play on the date, but is π worthy of its own day? Let’s be clear, π (and mathematics more broadly) does not have the same popularity of say, Star Wars, which is celebrated on two consecutive days in May: May the 4th (be with you) and Revenge of the 5th. This I get. The math is simple: Star Wars = Awesomeness! But Pi-day? Really?

## What is it about Pi?

On it’s surface, isn’t even that interesting. Indeed, π is simply the ratio of a circle’s circumference to its diameter. Yet, despite its simple definition,π is impossible to fully know. *π* is an irrational number – a number with an infinitely long, never repeating decimal sequence. This alone presents a great mystery, one that has motivated mathematicians for thousands of years and across civilizations to seek better methods for approximating. Billions of digits have been calculated.

## A Pi-day Math Problem

Perhaps most wondrous is that π reveals itself to us in many ways, not just as the ratio of circle’s circumference to its diameter. As an example, consider the following problem:

*What is the probability that two randomly chosen integers share no common factors?* Determining the answer to this problem is certainly not easy as there’s an infinite number of pairings that result when choosing the two integers at random. Amazingly a solution is known. Even more amazing is that the answer to this problem is exactly 6/π^{2 }(For this and more information on Pi then you can digest see Arndt, Jörg; Haenel, Christoph (2006). *Pi Unleashed*. Did you expect π would show up in the answer? I sure didn’t. The question posed is totally unrelated to anything I learned about circles.

We all have a basic sense that mathematics is more than we understand (some more than others). However, despite the difficulty mathematics presents, with time and effort more is revealed. Perhaps this is the appeal of Pi -day. *π* is the poster child for the mysteries of mathematics. For some, *π* is a story about mathematical theory and its incredible applications that are only unlocked with headache inducing effort and hardship. Check out Darren Aronofsky’s 1998 film π for tips on headache relief! In Yann Martel’s Man Booker Award winning book, Life of Pi, an Indian boy named Pi engages in Piphilology – the art of memorizing vast digits of π – in an effort to reclaim his identity from his peers. However, Pi is much more than this. Pi is seeking something greater, something mysterious, something beautiful. Some of us would argue that so too is mathematics and I guess that’s worthy of celebration. Cheers to Pi day.

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*Contributed by James Greenwood-Lee, Assistant Professor, Applied Mathematics at Athabasca University*