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.

Two-dimensional spirals

A two-dimensional spiral may be described using

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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).

Related Topics:
Polar coordinates - Radius - Continuous - Monotonic

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

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• The Archimedean spiral: r = a + bθ
• The Cornu spiral or clothoid
• Fermat's spiral: r = θ^1/2
• The hyperbolic spiral: r = a/θ
• The lituus: r = 1/θ^1/2
• The logarithmic spiral: r = ab^θ; approximations of this are found in nature