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A 'helix' (pl: 'helices'), from the Greek word ''έλικας/έλιξ'', is a twisted shape like a spring, screw or a spiral (correctly termed helical) staircase. Helices are important in biology, as DNA is helical and many proteins have helical substructures, known as alpha helices.
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.
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.
The 'pitch' of a helix is the width of one complete helix turn, measured along the helix axis.
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:
: $r\; =\; 1,,$
: $heta\; =\; t,,$
: $h\; =\; t.,$
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.
A helix has constant curvature and constant torsion.
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.
For a helix with thickness, see mathematical spring.
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.
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.

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See also

See also

★ DNA

★ Collagen

★ Helicoid

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★ Spiral (railway)