Spirals

In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.

Two major definitions of "spiral" in a respected American dictionary are:

Definition a describes a planar curve, that extends in both of the perpendicular directions within its plane; the groove on one side of a record closely approximates a plane spiral (and it is by the finite width and depth of the groove, but not by the wider spacing between than within tracks, that it falls short of being a perfect example); note that successive loops differ in diameter. In another example, the "center lines" of the arms of a spiral galaxy trace logarithmic spirals.

Definition b includes two kinds of 3-dimensional relatives of spirals:

In the side picture, the black curve at the bottom is an Archimedean spiral, while the green curve is a helix. The curve shown in red is a conic helix.

A two-dimensional spiral may be described most easily using polar coordinates, where the radius r is a monotonic continuous function of angle θ. The circle would be regarded as a degenerate case (the function not being strictly monotonic, but rather constant).

Some of the most important sorts of two-dimensional spirals include:

Archimedean spiral

Cornu spiral

Fermat's spiral

hyperbolic spiral

lituus

logarithmic spiral

spiral of Theodorus

Fibonacci Spiral (golden spiral)

The involute of a circle (black) is not identical to the Archimedean spiral (red).

For simple 3-d spirals, a third variable, h (height), is also a continuous, monotonic function of θ. For example, a conic helix may be defined as a spiral on a conic surface, with the distance to the apex an exponential function of θ.

...
Wikipedia