n. 1. any plane curve formed by a point winding round a fixed point at an ever-increasing distance from it, such as the curves in the figure below. The polar equation of an Archimedes spiral is r = aθ; of a logarithmic spiral, logr = aθ; and of a hyperbolic spiral, rθ = a, where a is a constant. Archimedes' and logarithmic spirals. 2. a helix in Euclidean space.