A hyperbolic spiral is a transcendental plane curve also known as a reciprocal spiral. It has the polar equation rθ = a, and is the inverse to the Archimedean spiral.
Hyperbolic spiral, for a=2.
It begins at an infinite distance from the pole in the centre, it winds faster and faster around as it approaches the pole, the distance from any point to the pole, following the curve, is infinite. The following is a parametric representation in Euclidean coordinates :
where t is a parameter. It has an asymptote at y = a.