Helix
- This article is about the shape. For the genus of terrestrial snails, see genus Helix.
A
helix 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.
We distinguish
right-handed and
left-handed helices. 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 2
&pi 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,
translationss, and changes of scale, all right-handed helices are equivalent to the helix defined above.