Helix

The right-handed helix (cos t, sin t, t) from t = 0 to 4π with arrowheads showing direction of increasing t

A helix (s/), plural helixes or helices (z/), is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helices are coil springs and the handrails of spiral staircases. A "filled-in" helix – for example, a "spiral" (helical) ramp – is called a helicoid.[1] Helices are important in biology, as the DNA molecule is formed as two intertwined helices, and many proteins have helical substructures, known as alpha helices. The word helix comes from the Greek word ἕλιξ, "twisted, curved".[2]

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.

Two types of helix shown in comparison. This shows the two chiralities of helices. One is left-handed and the other is right-handed. Each row compares the two helices from a different perspective. The chirality is a property of the object, not of the perspective (view-angle)

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.[3]

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[4] 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.[5]

Geometric pitch is the distance an element of an airplane propeller would advance in one revolution if it were moving along a helix having an angle equal to that between the chord of the element and a plane perpendicular to the propeller axis.

A curve is called a slant helix if its principal normal makes a constant angle with a fixed line in space.[6] It can be constructed by applying a transformation to the moving frame of a general helix.[7]

Some curves found in nature consist of multiple helices of different handedness joined together by transitions known as tendril perversions.

Other Languages
български: Винтова линия
čeština: Šroubovice
Cymraeg: Helics
dansk: Skruelinje
Deutsch: Helix
eesti: Heeliks
Ελληνικά: Έλικα
فارسی: پیچه
한국어: 나선
Bahasa Indonesia: Heliks
íslenska: Gormferill
Jawa: Heliks
magyar: Csavarvonal
Nederlands: Helix (wiskunde)
日本語: 螺旋
norsk: Heliks
norsk nynorsk: Heliks
Simple English: Helix
slovenščina: Vijačnica
српски / srpski: Хеликс
srpskohrvatski / српскохрватски: Heliks
suomi: Kierre
svenska: Helix
Türkçe: Sarmal
українська: Гвинтова лінія
粵語: 螺旋
中文: 螺旋