Spiral

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.

Three-dimensional spirals

As in the two-dimensional case, r is a continuous monotonic function of θ.

Related Topics:
Continuous - Monotonic

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For simple 3-d spirals, the third variable, h (height), is also a continuous, monotonic function of θ.

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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.

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For compound 3-d spirals, such as the spherical spiral described below,

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h increases with θ on one side of a point, and decreases with θ on the other side.

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The helix and vortex can be viewed as a kind of three-dimensional spiral.

Related Topics:
Helix - Vortex - Three-dimensional

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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 revolutions, with the distance between them decreasing as the curve approaches either of the poles.

Related Topics:
Rhumb line - Angle - Right angle - Longitude - Bearing - Infinite - Revolution

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