# Spirals

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Plane curves which usually go around one point (or around several points), moving either towards or away from it (them). One distinguishes two types: algebraic spirals and pseudo-spirals.

Algebraic spirals are spirals whose equations in polar coordinates are algebraic with respect to the variables and . These include the hyperbolic spiral, the Archimedean spiral, the Galilean spiral, the Fermat spiral, the parabolic spiral, and the lituus.

Pseudo-spirals are spirals whose natural equations can be written in the form

where is the radius of curvature and is the arc length. When , this is called the logarithmic spiral, when , the Cornu spiral, and when it is the evolvent of a circle (cf. Evolvent of a plane curve).

#### References

 [1] A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)