Many people celebrate Pi Day by eating pie. I prefer to celebrate it by being irrational.
In honour of Pi Day, I have hounded demanded of nicely asked my Official Statistician & Tattoo Consultant for some wise words about pi to share with you, my lovely readers1 So here, my friends, is some info on the wonder that is pi, from the wonder that is Almost Dr. Dan:
Not only is Pi irrational (i.e., it cannot be expressed as the ration of two integers), it is also transcendental. That is, it cannot be a zero (or root) of a polynomial equation with integer valued coefficients. For example, while root 2 is irrational, it is the solution to the following polynomial: x^2=2.
Other interesting Pi tidbits:
Indiana once had a ‘pi bill’ up for legislative discussion. Turns out an amateur mathematician thought he had proved how to square the circle. Sadly for him, it had already been shown that this was an impossibility in 1882 by von Lindemann. Strangely enough, people still to this day try to prove that you can square the circle. But I digress. The pi bill indirectly asserted that pi was in fact 3.2. Check out http://en.wikipedia.org/wiki/Indiana_Pi_Bill for full details.
I’ve also heard of other laws (but couldn’t verify the info) that had pi set to 4 (yikes!).
One of my favourite representations for pi is this rather simple looking infinite sum. It’s credited to Gregory and Leibniz.
As well, in honour of Pi Day, I give you this photo of Dan’s pi tattoo: