# The first lap of an Archmidean spiral

In polar coordinates, the Archimedean spiral is $r=\theta,\ \theta\ge0.$ Or maybe also $r= c\,\theta,\ \theta\ge0,$ where $c$ does not change as $\theta$ changes.

I found myself referring to that portion of the spiral in which $0\le\theta\le2\pi\text{ radians}$ as the "first lap", using the terminology of foot races.

Is there a standard term in geometry for that?

• I have worked with with spirals quite extensively and have never come across such a term. I usually think of them as rotations or turns (i.e., multiples of $2\pi$). I'll be curious to see if anyone comes up with something. – Cye Waldman Aug 12 '17 at 0:08