Based upon this column, I wondered: Do mathematicians spend time calculating numbers other than pi to an absurd number of digits? Is there something special about pi that wouldn’t apply to the square root of 2?
I don’t think there’s anything particularly special about pi other than that people have gotten romantically attached to it. Certainly, there are other important constants in mathematics but even sqrt(2) and e lag far behind pi in the amount of digits that have been calculated, according to Wikipedia.
There is a difference between √2 and π, in that, while they are both irrational, π is also transcendental. Just as √2 cannot be produced by any common fraction, π can’t be produced by taking any root of anything.
Also, every number has a square root, but only π is π.
Except, of course, for π^2. 
Actually, I’ve long thought it interesting that π gets all the attention, when I think 2π is really the more “natural” mathematical constant.
Because there are 2π radians in a circle? Well perhaps, but, on the other hand e[sup]iπ[/sup]+1 = 0, and the area of a circle is πr[sup]2[/sup]
Yeah, but e[sup]i2π[/sup]-1 = 0.
It’s not the root of any polynomial with rational coefficients. That’s weaker, of course, than not being the root of anything. It’s also stronger than “can’t be written in terms of nth roots of rationals”.
Sure, π is transcendental, but so are an infinite number of real numbers. In fact more are transcendental than are algebraic.
Yeah, but only √2 is √2. Only e is e. Insert any number you like.
Wow, all the things I thought of saying and then was too lazy to, Uncertain says. And our names are kinda similar, too…
I’ll note that in the alternative universe where people talked about K = 2π rather than π, people would be giving the formula for the area of a circle as Kr^2/4 and thinking nothing more of the fact that it’s not exactly Kr^2 than we do of the formula for circumference of a circle or volume of a sphere. They might also give Euler’s formula as e^(iK/2) + 1 = 0 and talk about how it relates the five great constants of math rather than the four great constants, or some such glurge.
The main reason that I think K is more natural is because it’s the one that’s actually the period of most of the functions that matter (sin, cos, e^(ix), other ways of saying the same things…).