# Why is Fermat's spiral formula written as $r^2=a^2\theta$ instead of $r=a\sqrt{\theta}$?

I'm reading Clifford A. Pickover's Math Book, in the Fermat's spiral page, it says the Fermat's spiral formula is $r^2=a^2\theta$, why isn't it written as $r=\pm a\sqrt{\theta}$? What's the problem in writing it that way?

-

Aesthetics: polynomial equations are usually nicer to work with. Probably a bit of tradition.

Also, $r = a \sqrt{\theta}$ is only half the spiral anyways: the other half is given by $r = -a \sqrt{\theta}$.

-
Yep, I noticed that when I evaluated it on Mathematica, to be precise, it would be $r=\pm a\sqrt \theta$. – Voyska Oct 14 '12 at 2:18
Can you comment about usually nicer to work with? – Voyska Oct 14 '12 at 2:20
It's one of those self-evident things that are hard to put words to. Solving for one variable as a function of the other frequently leads to much more complicated formulas, which is a hinderance in the common situation that you don't actually need things expressed that way. – Hurkyl Oct 14 '12 at 16:53
Can you provide me an example? – Voyska Oct 15 '12 at 7:39

The standard form works for all $a$ and $\theta$. It also eliminates the need to consider the different branches of the square root.

-