Blumenthal, Leonard M. Formerly, Department of Mathematics, University of Missouri, Columbia, Missouri.
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A term used generically to describe any geometrical entity that winds about a central point or axis while also receding from it. Spiral staircases, helices, nonplanar loxodromes (curves that intersect those of a given class at a constant angle, for example, rhumb lines, in case the curves are on a sphere whose meridians form the given class) are examples of spirals whose windings do not lie in a plane. The planar spiral curve ρ = aθ, in polar coordinates ρ and θ (see illustration), was introduced by Archimedes in his book On Spirals. Other planar spiral curves are logarithmic, ρ = eθ, the tangents to which make a constant angle with the radii vectors drawn to the points of contact; hyperbolic, ρθ = a; and the lituus, ρ2θ = a2. See also: Helix
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