A curve whose equation in polar coordinates is r = ae^kθ‎, where a > 0 and k are constants. Let O be the origin and P be any point on the curve. The curve derives its name from the property that the angle α‎ between OP and the tangent at P is constant. In fact, k = cotα‎. The curve is also called the logarithmic spiral.

Spiral with constant angle α‎

http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Erbas/KURSATgeometrypro/related%20curves/related%20curves.html Animations of related curves, and an interactive manipulation of the spiral in Geometer’s Sketchpad.