/spuy"reuhl/, n., adj., v., spiraled, spiraling or (esp. Brit.) spiralled, spiralling.n.1. Geom. a plane curve generated by a point moving around a fixed point while constantly receding from or approaching it.2. a helix.3. a single circle or ring of a spiral or helical curve or object.4. a spiral or helical object, formation, or form.5. Aeron. a maneuver in which an airplane descends in a helix of small pitch and large radius, with the angle of attack within that of the normal flight range.6. Football. a type of kick or pass in which the ball turns on its longer axis as it flies through the air.7. Econ. a continuous increase in costs, wages, prices, etc. (inflationary spiral), or a decrease in costs, wages, prices, etc. (deflationary spiral).adj.8. running continuously around a fixed point or center while constantly receding from or approaching it; coiling in a single plane: a spiral curve.9. coiling around a fixed line or axis in a constantly changing series of planes; helical.10. of or of the nature of a spire or coil.11. bound with a spiral binding; spiral-bound: a spiral notebook.v.i.12. to take a spiral form or course.13. to advance or increase steadily; rise: Costs have been spiraling all year.14. Aeron. to fly an airplane through a spiral course.v.t.15. to cause to take a spiral form or course.[1545-55; < ML spiralis, equiv. to L spir(a) coil ( < Gk speîra anything coiled, wreathed, or twisted; see SPIRE2) + -alis -AL1]
* * *plane curve that, in general, winds around a point while moving ever farther from the point. Many kinds of spiral are known, the first dating from the days of ancient Greece. The curves are observed in nature, and human beings have used them in machines and in ornament, notably architectural—for example, the whorl in an Ionic capital. The two most famous spirals are described below.Although Greek mathematician Archimedes did not discover the spiral that bears his name (see figure—>), he did employ it in his On Spirals (c. 225 BC) to square the circle (geometry) and trisect an angle (geometry). The equation of the spiral of Archimedes is r = aθ, in which a is a constant, r is the length of the radius from the centre, or beginning, of the spiral, and θ is the angular position (amount of rotation) of the radius. Like the grooves in a phonograph record, the distance between successive turns of the spiral is a constant—2πa, if θ is measured in radians.The equiangular, or logarithmic (logarithm), spiral (see figure—>) was discovered by the French scientist René Descartes (Descartes, René) in 1638. In 1692 the Swiss mathematician Jakob Bernoulli (Bernoulli, Jakob) named it spira mirabilis (“miracle spiral”) for its mathematical properties; it is carved on his tomb. The general equation of the logarithmic spiral is r = aeθ cot b, in which r is the radius of each turn of the spiral, a and b are constants that depend on the particular spiral, θ is the angle of rotation as the curve spirals, and e is the base of the natural logarithm. Whereas successive turns of the spiral of Archimedes are equally spaced, the distance between successive turns of the logarithmic spiral increases in a geometric progression (such as 1, 2, 4, 8,…). Among its other interesting properties, every ray from its centre intersects every turn of the spiral at a constant angle (equiangular), represented in the equation by b. Also, for b = π/2 the radius reduces to the constant a—in other words, to a circle of radius a. This approximate curve is observed in spider webs and, to a greater degree of accuracy, in the chambered mollusk, nautilus (see photograph—>), and in certain flowers.
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