Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 0 down vote favorite

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?

share|improve this question

2 Answers

up vote 2 down vote accepted

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 $r = -a \sqrt{\theta}$.

share|improve this answer
Yep, I noticed that when I evaluated it on Mathematica, to be precise, it would be $r=\pm a\sqrt \theta$. – Gustavo Bandeira Oct 14 '12 at 2:18
Can you comment about usually nicer to work with? – Gustavo Bandeira 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? – Gustavo Bandeira Oct 15 '12 at 7:39
up vote 2 down vote

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

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.