# Dictionary Definition

helix

### Noun

1 a curve that lies on the surface of a cylinder
or cone and cuts the element at a constant angle [syn: spiral]

2 a structure consisting of something wound in a
continuous series of loops; "a coil of rope" [syn: coil, spiral, volute, whorl]

3 type genus of the family Helicidae [syn:
genus
Helix] [also: helices (pl)]

# User Contributed Dictionary

### Pronunciation

- /ˈhiːlɪks/, /"hi:lIks/

### Noun

- A curve on the surface of a cylinder or cone such that its angle to a plane perpendicular to the axis is constant; the three-dimensional curve seen in a screw or a spiral staircase.
- A small volute under the abacus of a Corinthian capital.
- The incurved rim of the external ear.

#### Synonyms

- (curve): spiral (not in technical use)

#### Derived terms

#### Related terms

#### Translations

curve

- Czech: šroubovice
- Danish: skruelinje
- French: hélice
- Japanese: (, rasen)
- Swedish: helix

in architecture

a genus of land snail containing many
species

# Extensive Definition

A helix (pl: helices), from the Greek word
έλικας/έλιξ, is a three-dimensional, twisted shape. Common objects
formed like a helix are a spring, a
screw, and a
spiral staircase (though the last would be more correctly
called helical). Helices are important in biology, as the DNA molecule is formed
as two
intertwined helices, and many proteins have helical
substructures, known as alpha
helices.

## Types

Helices can be either right-handed or left-handed. With the line of sight being the helical axis, if clockwise movement of the helix corresponds to axial movement away from the observer, then it is a right-handed helix. If counter-clockwise movement corresponds to axial movement away from the observer, it is a left-handed helix. Handedness (or chirality) is a property of the helix, not of the perspective: a right-handed helix cannot be turned or flipped to look like a left-handed one unless it is viewed through a mirror, and vice versa.Here is another test for handedness: first grip
the helix with your right hand and direct your thumb parallel to
the axis of the helix. Then curl your fingers toward your palm,
following the path of the spiral as if the helix were a set of
rails that your fingers must slide along. If this causes your
entire hand to move in the same direction as your thumb is
pointing, then the helix is right-handed. If not, it is
left-handed. Try this test on the left-handed helix in the picture
below; in this case, your hand should move in the direction
opposite to the way your thumb points.

Most hardware screws are right-handed helices.
The alpha helix in biology as well as the A and B forms of DNA are
also right-handed helices. The Z form of DNA is
left-handed.

A double helix
typically consists geometrically of two congruent helices with the
same axis, differing by a translation along the axis, which may or
may not be half-way.

A conic helix may be defined as a spiral on a conic surface, with
the distance to the apex an exponential function of the angle
indicating direction from the axis. An example of a helix would be
the Corkscrew
roller coaster at Cedar Point amusement park.

A circular helix has constant curvature and constant
torsion.
The pitch of a helix is the width of one complete helix turn,
measured along the helix axis.

## Mathematics

In mathematics, a helix is a curve in 3-dimensional space. The following three equations in rectangular coordinates define a helix:- x = \cos(t),\,
- y = \sin(t),\,
- z = t.\,

As the parameter t increases, the
point (x,y,z) traces a right-handed helix of pitch 2π about the z-axis, in a right-handed
coordinate system.

In cylindrical
coordinates (r, θ, h), the same helix is described by:

- r = 1,\,
- \theta = t,\,
- h = t.\,

Another way of mathematically constructing a
helix is to plot a complex valued exponential function (e^xi)
taking imaginary arguments (see Euler's
formula).

Except for rotations, translations,
and changes of scale, all right-handed helices are equivalent to
the helix defined above. The equivalent left-handed helix can be
constructed in a number of ways, the simplest being to negate
either the x, y or z component.

The length of a general helix expressed in
rectangular coordinates as

- t\mapsto (a\cos t, a\sin t, bt), t\in [0,T]

## Examples

In music, pitch space is often modeled with helices or double helices, most often extending out of a circle such as the circle of fifths, so as to represent octave equivalency.helix in Bulgarian: Винтова линия

helix in Czech: Šroubovice

helix in Danish: Skruelinje

helix in German: Helix

helix in Spanish: Hélice (geometría)

helix in Galician: Hélice (xeometría)

helix in Indonesian: Heliks

helix in Italian: Elica (geometria)

helix in Hungarian: Csavarvonal

helix in Dutch: Helix (wiskunde)

helix in Norwegian: Helix

helix in Norwegian Nynorsk: Heliks

helix in Polish: Linia śrubowa

helix in Portuguese: Hélice (geometria)

helix in Russian: Винтовая линия

helix in Serbian: Хеликс

helix in Serbo-Croatian: Heliks

helix in Swedish: Helix

helix in Chinese: 螺旋