Note: I intentionally left the equation in the title in plain text instead of MathJax, so it is searchable.
Here is a spiral's equation in polar coordinates:
$$\theta=L/r,$$
and in Cartesian coordinates:
$$(x,y) = \left(r\cdot\cos\frac Lr,\, r\cdot\sin\frac Lr\right)$$
for $0 < r < \infty$ and some positive constant $L$.
It appeared here, at Math SE, as an answer to the Spiral equation question.
Does this curve have a name?
Best Answer
As @YvesDaoust said in a comment it is called a hyperbolic spiral, or a reciproke spiral as the circle inversion of an Archimedean spiral
Wikipedia has a couple of images, depending on whether you look at one or two arms of the hyperbola underlying $r=\frac a \varphi$