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?
Why is Fermat's spiral formula written as $r^2=a^2\theta$ instead of $r=a\sqrt{\theta}$?
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2 Answers
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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 $r = -a \sqrt{\theta}$.
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0Can you provide me an example? – 2012-10-15
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The standard form works for all $a$ and $\theta$. It also eliminates the need to consider the different branches of the square root.