Happy Pi Day!

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 Happy Pi Day!
Written by Mike James
Friday, 14 March 2014

Yes it is Pi day again, but this year it feels as though we aren't celebrating alone. For the first time it looks as if the momentum has built up to the point were a few people have heard about pi day and there are even attempts to sell you Pi connected items - as if it was a real holiday.

Today, assuming you are reading this on the 14th of March, is Pi day. Of course the date has been chosen because it is 3/14 i.e. third month 14th day and these are the first three digits of Pi. It has been some sort of official celebration in Russia for some years but in 2009 the US Congress joined in and announced National Pi day. Since then the celebrations have been growing and this year for the first time there have been some significant attempts to commercialize the holiday with special T shirts, mugs and so on. It has even managed to be a trending tag on Google+ for the first time.  It might be just a subjective judgement but this year Pi day seems to have a chance of breaking into the consciousness of the non-techie person.

So what is the fuss about?

Why bother celebrating Pi?

It's just the ratio of the diameter to the circumference of a circle, after all.

Well it might be, but it is a remarkable number that manages to wheedle its way into lots of formulas that you wouldn't expect to find it in.

Where's the circle in that - is the usual cry of first year STEM students.

For example, over on Sean Carroll's blog we have:

which is the field equation for general relativity. OK, there may be some tensors involved in this and it is complicated - but 8 pi?

Seriously? Pi manages to get itself into general relativity?

Carroll also reminds us that Pi day is Albert Einstein's birthday, so happy 135th Birthday in some proper time or other.

There are lots of other examples of Pi occurring in equations that it really doesn't seem to have a lot to do with, and the reason is usually that it's something to do with geometry - 2Pi radians in a complete rotation and 4Pi steradians in a sphere.

Pi also has connections with the difference between Euclidean and Non-Euclidean geometry and so on, but there are times when it appears in places that don't seem to have anything to do with geometry - just as the normalising factors in the normal distribution. If you look deep enough then you will find a the connection with geometry but sometimes that connection seems unreasonably deep.

Pi is threaded through math and technology like few other numbers.

In computer science it is special because it is one of the few computable real numbers. Most real numbers don't have programs that compute them for the simple reasons there are more reals than programs. Pi is regular in ways that make it very special while retaining the irregularities needed to make it an irrational transcendental number.

It is more the computational properties of Pi that make it special.

So Pi is a great number to pick to celebrate and to use as an educational tool. Unless, that is, you happen to prefer tau which is 2Pi and hence the ratio of the radius to the circumference. Tau is said to be a better choice of constant because it gets rid of the 2Pi that occurs in most 2D geometry-related formulas.

Of course, there is always some one wanting to spoil the party and this year it is Vi Hart who has a nice Anti-Pi Rant video. Don't take it too seriously, even though what she says is true:

By the way, the probability of picking any given number on the number line is zero and so Pi isn't special in this either. Vi is right that irrationals and transcendentals are in the majority of numbers but you need to keep in mind that there aren't many of then that also have nice regular algorithms that generate their digits.

So what do we do on Pi day?

This year you could track down one of those T Shirts or a mug or do the more traditional thing of eating as much pie as possible.