hyperbolic spiral


This spiral is a kind of Archimedean spiral.

The hyperbolic name reflects the relation between radius and angle being the same as the x,y relation for the hyperbola. This relationship leads also the name of the reciprocal spiral.
The curve is a Cotes' spiral.

When a hyperbolic spiral is rolling over a line, then the path of the pole forms a tractrix, being a roulette of the spiral.

Its inverse is the Archimides' spiral.

It was Pierre Varignon who studied the curve as first, in 1704. Later Johann Bernoulli (1710 - 1713) and Cotes (1722) worked on the curve.