Archimedean Spiral

An Archimedean spiral (also called the arithmetic spiral, or the spiral of Archimedes) is a curve named after the 3rd-century BC Greek mathematician Archimedes, who first described it. It is the locus of points corresponding to the position, over time, of a point moving away from a fixed center at a constant speed along a line that is itself rotating at a constant angular velocity — unlike a logarithmic spiral, successive turnings of an Archimedean spiral are always separated by the same fixed distance. In polar coordinates $(r, \theta)$ it is described by the equation:

$r = a + b\theta$