Helix facts for kids
In math, a helix is a curve in three dimensions. It looks a bit like a spiral. Each helix has a line called its axis. The helix has a constant angle to this line. Helices are often seen in nature and the sciences.
Types
Helices can be either right-handed or left-handed. With the line of sight along the helix's axis, if a clockwise screwing motion moves the helix away from the observer, then it is called a right-handed helix; if towards the observer, then 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 to look like a left-handed one unless it is viewed in a mirror, and vice versa.
Most hardware screw threads 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 height of one complete helix turn, measured parallel to the axis of the helix.
A double helix consists of two (typically congruent) helices with the same axis, differing by a translation along the axis.
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 is the Corkscrew roller coaster at Cedar Point amusement park.
A circular helix, (i.e. one with constant radius) has constant band curvature and constant torsion.
A curve is called a general helix or cylindrical helix if its tangent makes a constant angle with a fixed line in space. A curve is a general helix if and only if the ratio of curvature to torsion is constant.
A curve is called a slant helix if its principal normal makes a constant angle with a fixed line in space. It can be constructed by applying a transformation to the moving frame of a general helix.
Some curves found in nature consist of multiple helices of different handedness joined together by transitions known as tendril perversions.
Examples
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.
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Crystal structure of a folded molecular helix reported by Lehn et al. in Helv. Chim. Acta., 2003, 86, 1598–1624.
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A natural left-handed helix, made by a climber plant
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A charged particle in a uniform magnetic field following a helical path
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A helical coil spring
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A helix composed of sinusoidal x and y components
See also
In Spanish: Hélice (geometría) para niños
