- Spiral is also an album by Vangelis
In mathematics, a spiral is a curve which turns around
some central point or axis, getting progressively closer to or farther from it, depending on which way you follow the curve.
Two-dimensional spirals
A two-dimensional spiral may be described using polar
coordinates by saying that r is a continuous monotonic function of θ. The circle would be regarded as a degenerate case (the
function not being strictly monotonic, but rather constant).
Some of the more important sorts of two-dimensional spirals include:
Three-dimensional spirals
As in the two-dimensional case, r is a continuous monotonic function of θ.
For simple 3-d spirals, the third variable, h (height), is also a continuous, monotonic function of θ.
For compound 3-d spirals, such as the spherical spiral described below, h increases with θ on one side
of a point, and decreases with θ on the other side.
The helix can be viewed as a kind of three-dimensional spiral.
Spherical spiral
A spherical spiral is the curve on a sphere traced by a ship traveling from one pole to the other while keeping a
fixed angle (but not a right angle) with respect to the meridians of longitude
(cf. rhumb line). The curve has an infinite number of revolutions, with the
distance between them decreasing as the curve approaches either of the poles.
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