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spiral

  (spī'rəl) pronunciation
n.
    1. A curve on a plane that winds around a fixed center point at a continuously increasing or decreasing distance from the point.
    2. A three-dimensional curve that turns around an axis at a constant or continuously varying distance while moving parallel to the axis; a helix.
    3. Something having the form of such a curve: a spiral of black smoke.
  2. Printing. A spiral binding.
  3. The course or flight path of an object rotating on its longitudinal axis.
  4. A continuously accelerating increase or decrease: the wage-price spiral.
adj.
  1. Of or resembling a spiral.
  2. Circling around a center at a continuously increasing or decreasing distance.
  3. Coiling around an axis in a constantly changing series of planes; helical.
  4. Printing. Relating to or having a spiral binding: a spiral notebook.

v., -raled also -ralled, -ral·ing -ral·ling, -rals -rals.

v.intr.
  1. To take a spiral form or course.
  2. To rise or fall with steady acceleration.
v.tr.

To cause to take a spiral form or course.

[Medieval Latin spīrālis, of a spiral, from Latin spīra, coil. See spire2.]

spirality spi·ral'i·ty (spī-răl'ĭ-tē) n.
spirally spi'ral·ly adv.
 
 
Sci-Tech Encyclopedia: Spiral

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, and 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. See also Helix.

 
Thesaurus: spiral

verb

    To move or proceed on a repeatedly curving course: coil, corkscrew, curl, entwine, meander, snake, twine, twist, weave, wind2, wreathe. See repetition, straight/bent.

 
Antonyms: spiral

adj

Definition: curling, winding
Antonyms: straight, uncurling, unwinding

 
Architecture: spiral

A continuously wound reinforcement in the form of a cylindrical helix.

 
Veterinary Dictionary: spiral

1. winding like the thread of a screw.
2. a structure curving around a central point or axis.

  • Curschmann's s's — see curschmann's spirals.
  • s. organ of Corti — see organ of Corti.
  • s. penile deviation — a defect in bulls. See corkscrew penis.
  • s. septum — the arterial partition between aorta and pulmonary trunk, formed by the fusion of the truncal, bulbar and aorticopulmonary septa of the great vessels attached to the embryonic heart.
  • s. worm — Dispharynx nasuta. See synhimantus spiralis.
 
Word Tutor: spiral
pronunciation

IN BRIEF: Circling around a center in a curve that keeps growing larger or smaller.

pronunciation Pick up a pinecone and count the spiral rows of scales. — Stuart Kauffman

 
Wikipedia: spiral


For other senses of this word, see spiral (disambiguation).
Cutaway of a nautilus shell showing the chambers arranged in an approximately logarithmic spiral.
Enlarge
Cutaway of a nautilus shell showing the chambers arranged in an approximately logarithmic spiral.

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

An Archimedean spiral, a helix, and a conic spiral.
Enlarge
An Archimedean spiral, a helix, and a conic spiral.

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 ridges of 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 a few 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 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.

Two-dimensional spirals

A two-dimensional spiral may be described easiest 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:

Archimedean spiral

logarithmic spiral

Fermat's spiral

hyperbolic 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.

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:

Image:TORUSA-4 Konische Spirale entlang eines Kreises.PNG

This image is reminiscent of a Ouroboros symbol and could be mistaken for a torus with a continuously-increasing diameter:

Image:TORUSA-1 Torus mit variablem Ringdurchmesser.PNG

Spherical spiral

Archimedean Spherical Spiral
Enlarge
Archimedean 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 Newgrange entrance slab
Enlarge
The Newgrange entrance slab

The spiral plays a certain role in symbolism, and appears in megalithic art, notably in the Newgrange tomb. 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

Haeckel_Prosobranchia.jpg

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.

Thompson also studied spirals occurring in horns, teeth, claws and plants. [1]

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^{\circ}, r = c \sqrt{n}

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.[2]

References

  1. ^ Thompson, D'Arcy (1917,1942), On Growth and Form
  2. ^ Prusinkiewicz, Przemyslaw; Lindenmayer, Aristid (1990). The Algorithmic Beauty of Plants. Springer-Verlag, 101-107. ISBN 978-0387972978. 
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This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

 
Translations: Translations for: Spiral

Dansk (Danish)
adj. - spiral-, snegleformet, spiralformet, skruesnoet, vindelformet
n. - spiral, sneglevinding, sneglegang, skrue
v. intr. - hvirvle, sno
v. tr. - sno

idioms:

  • spiral staircase    vindeltrappe

Nederlands (Dutch)
spiraal, in spiraaltraject bewegen

Français (French)
adj. - spiral, en spirale, en hélice, en colimaçon, (reliure) spirale
n. - (gén, Math, Aviat) spirale, spirale (inflationniste), escalade (de)
v. intr. - (Écon) monter en flèche, monter/descendre en spirale ou en tournoyant, monter/descendre en vrille
v. tr. - faire monter en flèche ou en spirale

idioms:

  • spiral staircase    escalier en colimaçon

Deutsch (German)
n. - Spirale
v. - (sich) winden, in einer Spirale aufsteigen
adj. - spiralförmig

idioms:

  • spiral staircase    Wendeltreppe

Ελληνική (Greek)
n. - έλικας, σπείρα, σπείρωμα, σύστρεμμα, μαιανδρική σωλήνωση, σπιράλ
v. - στροβιλίζομαι, περιελίσσομαι
adj. - ελικοειδής, σπειροειδής, στριφτός

idioms:

  • spiral staircase    ελικοειδής σκάλα

Italiano (Italian)
formare una spirale, spirale

idioms:

  • spiral staircase    scale a chiocciola

Português (Portuguese)
n. - mola (f), espiral (f) (Mat.)
v. - espiralar, crescer rápida e incontroladamente
adj. - espiral

idioms:

  • spiral staircase    escada em caracol (f)

Русский (Russian)
спираль, виток, постепенно ускоряющееся падение или повышение, спиральный, закручивать в спираль, расти, остроконечный

idioms:

  • spiral staircase    винтовая лестница

Español (Spanish)
adj. - espiral, helicoidal, de caracol, en forma de chapitel o aguja
n. - espiral, hélice, espira, vuelo en espiral, curva de transición a ascenso
v. intr. - moverse en espiral, tomar forma espiral, volar en espiral
v. tr. - serpentear

idioms:

  • spiral staircase    escalera de caracol

Svenska (Swedish)
n. - spiral, snäcklinje
v. - göra spiralformig, röra sig i en spiral, gå upp i en spiral
adj. - spiralformig, snäckformig, spiral-, vindel-

中文（简体） (Chinese (Simplified))
螺旋的, 蜷线的, 螺线的, 盘旋的, 螺旋, 蜷线, 螺线, 螺旋形的东西, 盘旋, 螺旋形上升, 成螺旋形, 不断加剧地增加, 使成螺旋形, 使作螺旋形上升

idioms:

  • spiral staircase    螺旋式楼梯

中文（繁體） (Chinese (Traditional))
adj. - 螺旋的, 蜷線的, 螺線的, 盤旋的
n. - 螺旋, 蜷線, 螺線, 螺旋形的東西
v. intr. - 盤旋, 螺旋形上升, 成螺旋形, 不斷加劇地增加
v. tr. - 使成螺旋形, 使作螺旋形上升

idioms:

  • spiral staircase    螺旋式樓梯

한국어 (Korean)
adj. - 소용돌이 모양의, 나선형의, 와선의
n. - 나사선, 악순환, (미식 축구) 공이 장축을 중심으로 빙빙 돌도록 차기
v. intr. - 나선형으로 회전하다, (연기 등이) 소용돌이로 올라가다, (착실히) 증가하다
v. tr. - ~에 나사선 코스를 잡게 하다

日本語 (Japanese)
n. - 螺旋, らせん状のもの, 巻き貝, らせん状進行過程
adj. - らせん状の
v. - らせん形になる, らせん状に動く

idioms:

  • spiral staircase    らせん階段

العربيه (Arabic)
‏(الاسم) لولب, مسار حلزوني (فعل) يصعد و يهبط بشكل حلزوني (صفه) حلزوني, لولبي‏

עברית (Hebrew)
adj. - ‮בורגי, ספירלי, לולייני‬
n. - ‮סליל, תנועה בורגית‬
v. intr. - ‮הסתלסל, התחלזן‬
v. tr. - ‮עלה או נפל, בד"כ במהירות, סלסל‬

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Best of the Web: spiral

Some good "spiral" pages on the web:


American Sign Language
commtechlab.msu.edu
 
Math
mathworld.wolfram.com
 
 
 

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Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2007. Published by Houghton Mifflin Company. All rights reserved.  Read more
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Thesaurus. Roget's II: The New Thesaurus, Third Edition by the Editors of the American Heritage® Dictionary Copyright © 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved.  Read more
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Architecture. McGraw-Hill Dictionary of Architecture and Construction. Copyright © 2003 by McGraw-Hill Companies, Inc. All rights reserved.  Read more
Veterinary Dictionary. Saunders Comprehensive Veterinary Dictionary 3rd Edition. Copyright © 2007 by D.C. Blood, V.P. Studdert and C.C. Gay, Elsevier. All rights reserved.  Read more
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