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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 one follows the curve.
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TWO-DIMENSIONAL SPIRALS

A Two-dimensional spiral may be described using
Polar Coordinates by saying that the Radius ''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 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.

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 and Vortex can be viewed as a kind of Three-dimensional spiral.

For a helix with thickness, see Spring (math) .


Spherical spiral

A ''spherical spiral'' ( Rhumb Line ) 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 , i.e. keeping the same Bearing . The curve has an Infinite number of Revolution s, with the distance between them decreasing as the curve approaches either of the poles.