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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.

See also the horn torus asymptotic line.

Other link: mathematische-basteleien.de/spirale.htm

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© Robert FERRÉOL 2017