Helix
A helix , from the Greek word
????a?/????, 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.
Helices can be either right-handed or left-handed. If the curve of the helix moves from the lower left to the upper right, then it is a right-handed helix. If it moves from the lower right to the upper left, it is a left-handed helix. Handedness 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.
Encyclopedia
A
helix , from the Greek word
????a?/????, 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.
Helices can be either right-handed or left-handed. If the curve of the helix moves from the lower left to the upper right, then it is a right-handed helix. If it moves from the lower right to the upper left, it is a left-handed helix. Handedness 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 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
- y = sin
- z = t
Here
t is a real
parameter. As
t increases, the point traces a right-handed helix of pitch 2
p about the
z-axis, in a right-handed coordinate system.
In
cylindrical coordinates , the same helix is described by:
- r = 1
- ? = 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.
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 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.
See also
