# Dictionary Definition

spiral adj : in the shape of a coil [syn:
coiling, helical, spiraling, volute, voluted, whorled, turbinate]

### Noun

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

### Verb

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"

# User Contributed Dictionary

### Noun

#### Related terms

#### Translations

helix

- Finnish: kierre

### Verb

(UK) (US)- 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.

## Northern Sami

### Noun

spiral# Extensive Definition

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 helix

A "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 spirals

A 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 spirals

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.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 spiral

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 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 symbol

The 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 nature

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 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

## References

## See also

- Seashell surface
- Celtic maze (straight-line spiral)

## External links

- 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

# Synonyms, Antonyms and Related Words

Milky Way, O-shaped, Via Lactea, acrobatics, aerobatics, ambagious, anfractuous, arise, ascend, aspire, backhanded, bank, banking, barred spiral, barred
spiral galaxy, become airborne, chandelle, circle, circling, circuit, circuiteer, circuition, circuitous, circuitousness, circuitry, circular, circularity, circulate, circulation, circumambience, circumambiency, circumambulate, circumambulation,
circumflexion,
circumlocution,
circummigrate,
circummigration,
circumnavigate,
circumnavigation,
circumvent, cirrus, claw skyward, close the
circle, cochlear,
cochleate, coil, coiled, come full circle, come
up, compass, corkscrew, corkscrewy, cosmic noise,
crab, crabbing, curl, curl upwards, curlicue, cycle, describe a circle, deviance, deviancy, deviating, deviation, deviative, devious, deviousness, digression, digressive, dip, discursive, dive, diving, encircle, encompass, entwine, evolute, excursion, excursive, excursus, feather, fishtail, fishtailing, flank, float, fly, fly aloft, gain altitude,
galactic circle, galactic cluster, galactic coordinates, galactic
latitude, galactic longitude, galactic nebula, galactic noise,
galactic pole, galaxy,
girdle, girdle the globe,
glide, go about, go
around, go round, go the round, go up, grow up, gyre, gyring, hang, helical, helicoid, helix, hover, indirect, indirection, involute, island universe,
kink, kite, lap, leave the ground, levitate, loom, loop, make a circuit, meandering, mount, nose dive, oblique, orbit, orbital, orbiting, out-of-the-way,
plane, plow, poise, porpoise, power dive, pull out,
pull up, pull-up, pullout, push down, pushdown, rear, rear up, revolve, ringlet, rise, rise up, roll, rolling, rotary, round, roundabout, roundaboutness, rounding, screw, screw-shaped, scroll, scrolled, sideslip, skid, skirt, soar, spheroidal galaxy, spin, spiral galaxy, spiral nebula,
spiraling, spire, spiroid, stall, stand up, stunt, stunting, supergalaxy, surge, surround, swarm up, sweep up,
swirl, tactical maneuvers,
take off, tendril,
tower, turbinal, turbinate, turn, turning, twine, twirl, twist, undulate, up, upgo, upgrow, upheave, uprise, upspin, upstream, upsurge, upswarm, upwind, verticillate, volplane, volute, voluted, volution, vortex, wheel, wheeling, whirl, whorl, whorled, wreathe, yaw, zoom