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Helical)
- This article is about the shape. See helix (disambiguation) for other meanings.
A helix (pl: helices), from the Greek word έλικας/έλιξ, is a twisted shape like a spring, screw or a spiral staircase. Helices are important in biology, as DNA is helical and many proteins have helical substructures, known as alpha helices.
A left-handed and a right-handed helix.
Right-handed and left-handed helices can be distinguished from each other. If you move along a helix in the direction of your right hand's thumb, and the helix turns in the direction of your right hand's fingers, then it's a right-handed helix, otherwise a left-handed one. Another way to visualize this distinction: picture the helix vertical; if the front strands move from the lower left to the upper right, then it is a right-handed helix. Note that handedness (or chirality) is a property of the helix, not of the perspective: you can turn a right-handed helix around and it's still right-handed.
Most 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 length 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
Here t is a real parameter. As 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
- θ = h
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.
In music pitch space is often modeled with helixes or double helixes, most often extending out of a circle such as the circle of fifths, so as to represent octave equivalency.
