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spiral (adj.)
1.in the shape of a coil
spiral (n.)
1.flying downward in a helical path with a large radius
2.a structure consisting of something wound in a continuous series of loops"a coil of rope"
3.ornament consisting of a curve on a plane that winds around a center with an increasing distance from the center
4.a plane curve traced by a point circling about the center but at increasing distances from the center
5.a curve that lies on the surface of a cylinder or cone and cuts the element at a constant angle
6.a continuously accelerating change in the economy
spiral (v. intr.)
1.to wind or move in a spiral course"the muscles and nerves of his fine drawn body were coiling for action" "black smoke coiling up into the sky" "the young people gyrated on the dance floor"
2.move in a spiral or zigzag course
3.form a spiral"The path spirals up the mountain"
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Merriam Webster
SpiralSpi"ral (?), a. [Cf. F. spiral. See Spire a winding line.]
1. Winding or circling round a center or pole and gradually receding from it; as, the spiral curve of a watch spring.
2. Winding round a cylinder or imaginary axis, and at the same time rising or advancing forward; winding like the thread of a screw; helical.
3. (Geom.) Of or pertaining to a spiral; like a spiral.
Spiral gear, or Spiral wheel (Mach.), a gear resembling in general a spur gear, but having its teeth cut at an angle with its axis, or so that they form small portions of screws or spirals. -- Spiral gearing, a kind of gearing sometimes used in light machinery, in which spiral gears, instead of bevel gears, are used to transmit motion between shafts that are not parallel. -- Spiral operculum, an operculum whih has spiral lines of growth. -- Spiral shell, any shell in which the whorls form a spiral or helix. -- Spiral spring. See the Note under Spring, n., 4.
SpiralSpi"ral (?), n. [Cf. F. spirale. See Spiral, a.]
1. (Geom.) A plane curve, not reëntrant, described by a point, called the generatrix, moving along a straight line according to a mathematical law, while the line is revolving about a fixed point called the pole. Cf. Helix.
2. Anything which has a spiral form, as a spiral shell.
Equiangular spiral,a plane curve which cuts all its generatrices at the same angle. Same as Logarithmic spiral, under Logarithmic. -- Spiral of Archimedes, a spiral the law of which is that the generatrix moves uniformly along the revolving line, which also moves uniformly.
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Voir aussi
⇨ Spiral CT • Spiral Computed Tomography • Spiral Cone-Beam CT • Spiral Cone-Beam Computed Tomography • Spiral Ganglia • Spiral Ganglion • Spiral Lamina • Spiral Organ • Spiral Volume CT • Spiral Volumetric CT • Tomography, Spiral Computed • Tomography, Spiral Volumetric Computed • deflationary spiral • inflationary spiral • spiral angle • spiral bandage • spiral drill • spiral galaxy • spiral nebula • spiral ratchet screwdriver • spiral spring • spiral staircase • spiral-shelled
⇨ 2009 Norwegian spiral anomaly • Archimedean spiral • Barless Magellanic spiral • Barless Magellanic spiral galaxies • Barless Magellanic spiral galaxy • Barred Magellanic spiral • Barred Magellanic spiral galaxies • Barred Magellanic spiral galaxy • Barred Spiral Galaxies • Barred Spiral galaxies • Barred spiral galaxy • Barred-spiral galaxy • Bethungra Spiral • Broken Circle / Spiral Hill EP • Charlotte spiral • Cochlear spiral • Concho-spiral • Cornu spiral • Cornu's spiral • Cougal Spiral (railway) • Death spiral • Death spiral (figure skating) • Death spiral (insurance) • Death spiral financing • Deviancy amplification spiral • Downwarde Spiral • Dunderberg Spiral Railway • Dwarf spiral galaxy • Ekman spiral • Electron spiral toroid • False Spiral • False spiral • Fermat spiral • Fermat's spiral • Fraser spiral illusion • Fraser's spiral • Further Down the Spiral • Golden spiral • Grand design spiral galaxy • Graveyard spiral • Hell Spiral • Hyperbolic spiral • Intermediate Magellanic barred spiral galaxies • Intermediate Magellanic barred spiral galaxy • Intermediate Magellanic spiral galaxies • Intermediate Magellanic spiral galaxy • Intermediate barred Magellanic spiral galaxies • Intermediate barred Magellanic spiral galaxy • Intermediate barred spiral galaxies • Intermediate barred spiral galaxy • Intermediate spiral galaxies • Intermediate spiral galaxy • Lentulo spiral • List of Magellanic barred spiral galaxies • List of Magellanic intermediate barred spiral galaxies • List of Magellanic intermediate spiral galaxies • List of Magellanic spiral galaxies • List of Spiral characters • List of ancient spiral stairs • List of barless Magellanic spiral galaxies • List of barred Magellanic spiral galaxies • List of intermediate Magellanic spiral galaxies • List of intermediate barred Magellanic spiral galaxies • List of spiral galaxies • List of unbarred Magellanic spiral galaxies • Live in an American Time Spiral • Logarithmic spiral • Logarithmic spiral beaches • Magellanic barred spiral • Magellanic barred spiral galaxies • Magellanic barred spiral galaxy • Magellanic intermediate barred spiral galaxies • Magellanic intermediate barred spiral galaxy • Magellanic intermediate spiral galaxies • Magellanic intermediate spiral galaxy • Magellanic spiral • Magellanic spiral galaxies • Magellanic spiral galaxy • Mode Gakuen Spiral Towers • Mugen Spiral • Osseous spiral lamina • Padovan cuboid spiral • Parker spiral • Price/wage spiral • Prime spiral • Raurimu Spiral • Reciprocal Spiral • Sacks spiral • Shchelkin spiral • Spiral (1978 film) • Spiral (2007 film) • Spiral (Buffy the Vampire Slayer) • Spiral (TV series) • Spiral (X-men) • Spiral (album) • Spiral (bobsleigh, luge, and skeleton) • Spiral (building) • Spiral (comics) • Spiral (dinghy) • Spiral (disambiguation) • Spiral (novel) • Spiral (piercing) • Spiral (process composition) • Spiral (railway) • Spiral (song) • Spiral / Ulterior Motive • Spiral Architect (disambiguation) • Spiral Ascent • Spiral Beach • Spiral CT • Spiral Castle • Spiral Castle (album) • Spiral Circle Complete • Spiral Circus • Spiral Dance (band) • Spiral Diner • Spiral Dynamics • Spiral Galaxies • Spiral Galaxy M104 • Spiral Galaxy NGC 4435 • Spiral Galaxy NGC 4438 • Spiral Galaxy NGC 7318 • Spiral Galaxy NGC 7318B • Spiral Galaxy UGC 12100 • Spiral Honey • Spiral Island • Spiral Jetty • Spiral Live at Montreux 1978 • Spiral Q Puppet Theater • Spiral Scratch • Spiral Scratch (Doctor Who) • Spiral Scratch (EP) • Spiral Spiders • Spiral Staircase • Spiral Staircase (Ralph McTell album) • Spiral Staircase – Classic Songs • Spiral Stairs • Spiral Starecase • Spiral Tribe • Spiral Universe • Spiral Walls Containing Autumns of Light • Spiral Zone • Spiral approach • Spiral arm • Spiral bevel gear • Spiral bound • Spiral dance • Spiral development • Spiral didgeridoo • Spiral fracture • Spiral galaxies • Spiral galaxy • Spiral ganglion • Spiral hornsnail • Spiral ligament • Spiral limbus • Spiral model • Spiral nebulae • Spiral of Life • Spiral of silence • Spiral pump • Spiral saw • Spiral separator • Spiral sliced meat • Spiral spaceplane • Spiral staircase • Spiral tube water wheel • Spiral tufted bryozoa • Spiral tunnels and tunnels on a curved alignment • Spiral valve • Spiral valves of Heister • Spiral ~Suiri no Kizuna~ • The Downward Spiral • The Inexperienced Spiral Traveller • The Mystery of the Spiral Bridge • The Spiral Astana • The Spiral Dance • The Spiral Notebook • The Spiral Road • The Spiral Staircase • The Spiral Staircase (1975 film) • The Spiral Staircase (2000 film) • Time Spiral • Time spiral • Triple spiral • Ulam spiral • Unbarred Magellanic spiral • Unbarred Magellanic spiral galaxies • Unbarred Magellanic spiral galaxy • Unbarred spiral galaxies • Unbarred spiral galaxy • Upward Spiral • Visions from the Spiral Generator • Wage/price spiral
spiral (adj.)
coiled[Similaire]
spiral (n.)
rotary motion, rotation[Hyper.]
corkscrew, spiral[Dérivé]
spiral (n.)
spiral (n.)
ornement architectural (fr)[ClasseParExt.]
spiral (n.)
curve, curved shape[Hyper.]
coil, gyrate, spiral - spiral[Dérivé]
spiral (n.)
ligne courbe (géométrie) (fr)[Classe]
ornement architectural (fr)[ClasseParExt.]
ligne courbe (fr)[Classe]
hélice (fr)[termes liés]
(Jew; Yid), (Judaism)[termes liés]
autre élément d'une colonne (fr)[DomainDescrip.]
curve, curved shape[Hyper.]
spiral[Dérivé]
spiral (n.)
economic process[Hyper.]
spiral (v. intr.)
spiral (v. intr.)
spiral (v. intr.)
curve, twist, wind[Hyper.]
loop, spiral - helix, spiral[Dérivé]
Wikipedia
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (July 2007) |
In mathematics, a spiral is a curve which emanates from a central point, getting progressively farther away as it revolves around the point.
Contents |
While a "spiral" and a "helix" are distinct as technical terms, a helix is sometimes described as a spiral in non-technical usage. The two primary definitions of a spiral are provided by the American Heritage Dictionary:[1]
a. A curve on a plane that winds around a fixed center point at a continuously increasing or decreasing distance from the point.
b. A three-dimensional curve that turns around an axis at a varying distance while moving parallel to the axis.
The first definition is for a planar curve that extends primarily in length and width, but not in height. A groove on a record[2] or the arms of a spiral galaxy (a Logarithmic spiral) are examples of a spiral.
The second definition is for the 3-Dimensional variant of a spiral, for example a conical spring (device) can be described as a spiral whereas a cylindrical spring or strand of a DNA are examples of a helix.[1]
The length and width of a helix typically remain static and do not grow like on a planar spiral. If they do, then the helix becomes a conic helix. You can make a conic helix with an Archimedean or equiangular spiral by giving height to the center point, thereby creating a cone-shape from the spiral.[3]
In the side picture, the black curve at the bottom is an Archimedean spiral, while the green curve is a helix. A cross between a spiral and a helix, such as the curve shown in red, is known as a conic helix. The spring used to hold and make contact with the negative terminals of AA or AAA batteries in remote controls and the vortex that is created when water is draining in a sink are examples of conic helices.
A two-dimensional spiral may be described most easily using polar coordinates, where the radius r is a monotonic continuous function of angle 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:
For simple 3-d spirals, a 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.
The helix and vortex can be viewed as a kind of three-dimensional spiral.
For a helix with thickness, see spring (math).
Another kind of spiral is a conic spiral along a circle. This spiral is formed along the surface of a cone whose axis is bent and restricted to a circle:
This image is reminiscent of a Ouroboros symbol and could be mistaken for a torus with a continuously-increasing diameter:
A spherical spiral (rhumb line or loxodrome, left picture) is the curve on a sphere traced by a ship traveling from one pole to the other while keeping a fixed angle (unequal to 0° and to 90°) 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.
The gap between the curves of an Archimedean spiral (right picture) remains constant as the radius changes and hence is not a rhumb line.
The spiral plays a specific role in symbolism, and appears in megalithic art, notably in the Newgrange tomb or in many Galician petroglyphs such as the one in Mogor. See, for example, the triple spiral.
While scholars are still debating the subject, there is a growing acceptance that the simple spiral, when found in Chinese art, is an early symbol for the sun. Roof tiles dating back to the Tang Dynasty with this symbol have been found west of the ancient city of Chang'an (modern-day Xian).
Spirals are also a symbol of hypnosis, stemming from the cliché of people and cartoon characters being hypnotized by staring into a spinning spiral (one example being Kaa in Disney's The Jungle Book). They are also used as a symbol of dizziness, where the eyes of a cartoon character, especially in anime and manga, will turn into spirals to show they are dizzy or dazed. The spiral is also found in structures as small as the double helix of DNA and as large as a galaxy. Because of this frequent natural occurrence, the spiral is the official symbol of the World Pantheist Movement.[4]
The spiral is also a symbol of the process of dialectic.
The study of spirals in nature have a long history, Christopher Wren observed that many shells form a logarithmic spiral. Jan Swammerdam observed the common mathematical characteristics of a wide range of shells from Helix to Spirula and Henry Nottidge Moseley described the mathematics of univalve shells. D’Arcy Wentworth Thompson's On Growth and Form gives extensive treatment to these spirals. He describes how shells are formed by rotating a closed curve around a fixed axis, the shape of the curve remains fixed but its size grows in a geometric progression. In some shell such as Nautilus and ammonites the generating curve revolves in a plane perpendicular to the axis and the shell will form a planar discoid shape. In others it follows a skew path forming a helico-spiral pattern.
Thompson also studied spirals occurring in horns, teeth, claws and plants.[5]
Spirals in plants and animals are frequently described as whorls. This is also the name given to spiral shaped fingerprints.
A model for the pattern of florets in the head of a sunflower was proposed by H Vogel. This has the form
where n is the index number of the floret and c is a constant scaling factor, and is a form of Fermat's spiral. The angle 137.5° is related to the golden ratio and gives a close packing of florets.[6]
The spiral has inspired artists throughout the ages. Among the most famous of spiral-inspired art is Robert Smithson's earthwork, "Spiral Jetty", at the Great Salt Lake in Utah. The spiral theme is also present in David Wood's Spiral Resonance Field at the Balloon Museum in Albuquerque, as well as in the critically acclaimed Nine Inch Nails 1994 concept album The Downward Spiral. The Spiral is also a prominent theme in the anime Gurren Lagann, where it represents a philosophy and way of life.
Spirals was also the source of material for Japanese horror manga artist Junji Ito for his manga Uzumaki about a town obsessed with spirals, which was adapted to a feature film in 2000.
Wikimedia Commons has media related to: Spiral |
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