SPIRAL

A plane spiral is a curve having a polar equation of the type where f is monotone on an unbounded interval. The spirals are necessarily transcendental curves.

Examples:
- the logarithmic spiral.
- the spirals with equation (sometimes called Archimedean spiral of index n):
- the Archimedean spiral (n =1) and its cousin the evolute of a circle.
- the hyperbolic spiral (n = –1)
- the Fermat spiral (n = 1/2) (special case of parabolic spiral)
- the lituus (n = –1/2)
- a special case of Galilean spiral (n = 2),
- the sinusoidal spirals, the pseudo-spirals of Pirondini, which cannot be spirals in the above sense.
- the anallagmatic spirals.
- the tractrix spiral.
- the Poinsot spiral.
- the spiral of the hyperbolic tangent.
- the balance spring curve.
- the Cornu spiral.
- the Sici spiral.
- the rotating rod spiral.
- the Norwich spiral, the Sturm spiral.
- certain cases of epispirals.

To these planar spirals can be added the conical spirals of Pappus and of Pirondini, the spherical spirals (or clelias), which are 3D curves.