Helix

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 Protein s have helical substructures, known as Alpha Helices .

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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- Dimension al 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 2 π 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 Rotation s, Translation s, 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 Double Helix typically consists geometrically of two congruent helixes 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 Spring (math) .

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 .

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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.

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Helix