spiral adj : in the shape of a coil [syn: coiling, helical, spiraling, volute, voluted, whorled, turbinate]
1 a plane curve traced by a point circling about the center but at ever-greater distances from it
2 a curve that lies on the surface of a cylinder or cone and cuts the element at a constant angle [syn: helix]
3 ornament consisting of a curve on a plane that winds around a center with an increasing distance from the center [syn: volute]
4 a structure consisting of something wound in a continuous series of loops; "a coil of rope" [syn: coil, volute, whorl, helix]
5 flying downward in a helical path with a large radius
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" [syn: gyrate, coil]
2 form a spiral; "The path spirals up the mountain"
- /ˈspaɪɹəl/, /"spaIr@l/
- Rhymes: -aɪrəl
- Finnish: kierre
- To move along the path of a spiral or helix.
- The falling leaves spiralled down from the tree.
- To increase continually.
- Her debts were spiralling out of control.
In mathematics, a spiral is a curve which emanates from a central point, getting progressively farther away as it revolves around the point.
Spiral or helixA "spiral" and a "helix" are two terms that are easily confused, but represent different objects.
A spiral is typically a planar curve (that is, flat), like the groove on a record or the arms of a spiral galaxy. A helix, on the other hand, is a three-dimensional coil that runs along the surface of a cylinder, like a screw. There are many instances where in colloquial usage spiral is used as a synonym for helix, notably spiral staircase and spiral binding of books. Mathematically this is incorrect but the terms are increasing in common usage.
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. An example of a conic helix is the spring used to hold and make contact with the negative terminals of AA or AAA batteries in remote controls.
Two-dimensional spiralsA two-dimensional spiral may be described most easily using polar coordinates, where the radius r is a continuous monotonic 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:
- The Archimedean spiral: r = a + bθ
- The Cornu spiral or clothoid
- Fermat's spiral: r = θ1/2
- The hyperbolic spiral: r = a/θ
- The lituus: r = 1/θ1/2
- The logarithmic spiral: r = abθ; approximations of this are found in nature
- The Fibonacci spiral and golden spiral: special cases of the logarithmic spiral.
Three-dimensional spiralsFor 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.
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:
Spherical spiralA 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 curve progresses across the surface of the sphere. Therefore, this line has finite length. Notice that this is not the same thing as the rhumb line described earlier.
As a symbolThe spiral plays a certain 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 also 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).
The spiral is the most ancient symbol found on every civilized continent. Due to its appearance at burial sites across the globe, the spiral most likely represented the "life-death-rebirth" cycle. Similarly, the spiral symbolized the sun, as ancient people thought the sun was born each morning, died each night, and was reborn the next morning.
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.
In natureThe 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 pirpendicular to the axis and the shell will form a planer discoid shape. In others it follows a skew path forming a helico-spiral pattern.
Spirals in plants and animals are frequently described as whorls.
A model for the pattern of florets in the head of a sunflower was proposed by H Vogel. This has the form
- \theta = n \times 137.5^, r = c \sqrt
- SpiralZoom.com, an educational website about the science of pattern formation, spirals in nature, and spirals in the mythic imagination.
spiral in Bosnian: Spirala
spiral in Bulgarian: Спирала
spiral in Czech: Spirála
spiral in Danish: Spiral
spiral in German: Spirale
spiral in Spanish: Espiral
spiral in Esperanto: Spiralo
spiral in French: Spirale
spiral in Croatian: Spirala
spiral in Italian: Spirale
spiral in Hebrew: ספירלה
spiral in Hungarian: Spirál
spiral in Dutch: Spiraal
spiral in Japanese: 螺旋
spiral in Norwegian: Spiral
spiral in Portuguese: Espiral
spiral in Russian: Спираль
spiral in Slovak: Špirála (matematika)
spiral in Slovenian: Spirala
spiral in Finnish: Spiraali
spiral in Swedish: Spiral
spiral in Chinese: 螺线
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