A helix (pl: helices), from the Greek word έλικας/έλιξ, is a three-dimensional, twisted shape. Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly Common objects formed like a helix are a spring, a screw, and a spiral staircase (though the last would be more correctly called helical). A spring is a flexible elastic object used to store mechanical Energy. A screw is a shaft with a helical groove or thread formed on its surface and provision at one end to turn the screw [1][2] 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. Foundations of modern biology There are five unifying principles Deoxyribonucleic acid ( DNA) is a Nucleic acid that contains the genetic instructions used in the development and functioning of all known In Geometry a double helix (plural helices) typically consists of two congruent helices with the same axis differing by a translation Proteins are large Organic compounds made of Amino acids arranged in a linear chain and joined together by Peptide bonds between the Carboxyl A common motif in the Secondary structure of Proteins the alpha helix (α-helix is a right-handed coiled conformation resembling a spring, in which
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Types
Helices can be either right-handed or left-handed. With the line of sight being the helical axis, if clockwise movement of the helix corresponds to axial movement away from the observer, then it is a right-handed helix. If counter-clockwise movement corresponds to axial movement away from the observer, 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 or flipped to look like a left-handed one unless it is viewed through a mirror, and vice versa. In Geometry, a figure is chiral (and said to have chirality) if it is not identical to its Mirror image, or more particularly if it cannot be mapped to
Here is another test for handedness: first grip the helix with your right hand and direct your thumb parallel to the axis of the helix. Then curl your fingers toward your palm, following the path of the spiral as if the helix were a set of rails that your fingers must slide along. If this causes your entire hand to move in the same direction as your thumb is pointing, then the helix is right-handed. If not, it is left-handed. Try this test on the left-handed helix in the picture below; in this case, your hand should move in the direction opposite to the way your thumb points.
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. A-DNA is one of the many possible double helical structures of DNA. Deoxyribonucleic acid ( DNA) is a Nucleic acid that contains the genetic instructions used in the development and functioning of all known The Z form of DNA is left-handed. Z-DNA is one of the many possible double helical structures of DNA.
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. In Geometry a double helix (plural helices) typically consists of two congruent helices with the same axis differing by a translation [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. In Mathematics, a spiral is a Curve which emanates from a central point getting progressively farther away as it revolves around the point An example of a helix would be the Corkscrew roller coaster at Cedar Point amusement park. Corkscrew is a Roller coaster at the Cedar Point Amusement park in Sandusky Ohio.
A circular helix has constant curvature and constant torsion. In Mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry The pitch of a helix is the width of one complete helix turn, measured along the helix axis.
Mathematics
In mathematics, a helix is a curve in 3-dimensional space. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and This article only considers curves in Euclidean space Most of the notions presented here have analogues for curves in Riemannian and pseudo-Riemannian In mathematics the dimension of a Space is roughly defined as the minimum number of Coordinates needed to specify every point within it The following three equations in rectangular coordinates define a helix[4]:
As the parameter t increases, the point (x,y,z) traces a right-handed helix of pitch 2π about the z-axis, in a right-handed coordinate system. In Mathematics, the Cartesian coordinate system (also called rectangular coordinate system) is used to determine each point uniquely in a plane In Mathematics, Statistics, and the mathematical Sciences a parameter ( G auxiliary measure) is a quantity that defines certain characteristics IMPORTANT NOTICE Please note that Wikipedia is not a database to store the millions of digits of π please refrain from adding those to Wikipedia as it could cause technical problems
In cylindrical coordinates (r, θ, h), the same helix is described by:
Another way of mathematically constructing a helix is to plot a complex valued exponential function (e^xi) taking imaginary arguments (see Euler's formula). The cylindrical coordinate system is a three-dimensional Coordinate system which essentially extends circular polar coordinates by adding a third coordinate (usually This article is about Euler's formula in Complex analysis. For Euler's formula in algebraic topology and polyhedral combinatorics see Euler characteristic
Except for rotations, translations, and changes of scale, all right-handed helices are equivalent to the helix defined above. A rotation is a movement of an object in a circular motion A two- Dimensional object rotates around a center (or point) of rotation In Euclidean geometry, a translation is moving every point a constant distance in a specified direction 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.
The length of a general helix expressed in rectangular coordinates as
![t\mapsto (a\cos t, a\sin t, bt), t\in [0,T]](../../../../math/b/3/3/b330929a1f1e9a4e8a1c6b79f346fc8b.png)
equals 
, its curvature is 
and its torsion is 
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. Music is an Art form in which the medium is Sound organized in Time. In Music theory, pitch spaces model relationships between pitches In Music theory, the circle of fifths (or '''circle of fourths''') shows the relationships among the twelve tones of the Chromatic scale, their corresponding In Music, an octave ( is the the use of which is "common in most musical systems
References
- ^ "Helices" by Sándor Kabai, The Wolfram Demonstrations Project.
- ^ "Helical Staircase" by Sándor Kabai, The Wolfram Demonstrations Project.
- ^ "Double Helix" by Sándor Kabai, The Wolfram Demonstrations Project.
- ^ Eric W. Weisstein, Helix at MathWorld. Eric W Weisstein (born March 18, 1969, in Bloomington Indiana) is an Encyclopedist who created and maintains MathWorld MathWorld is an online Mathematics reference work created and largely written by Eric W
See also
Collagen is the main Protein of Connective tissue in Animals and the most abundant protein in Mammals making up about 50% of the whole-body protein The helicoid, after the plane and the Catenoid, is the third Minimal surface to be known Symmetry generally conveys two primary meanings The first is an imprecise sense of harmonious or aesthetically-pleasing proportionality and balance such that it reflects beauty or A spiral (sometimes called a spiral loop or just loop) is a technique employed by Railways to ascend steep hills In mathematics a seashell surface is a surface made by a circle which spirals up the z -axis while decreasing its own radius and distance from the z -axis A common motif in the Secondary structure of Proteins the alpha helix (α-helix is a right-handed coiled conformation resembling a spring, in whichDictionary
helix
-noun
- (mathematics) A curve on the surface of a cylinder or cone such that its angle to a plane perpendicular to the axis is constant; the three-dimensional curve seen in a screw or a spiral staircase.
- (architecture) A small volute under the abacus of a Corinthian capital.
- (anatomy) The incurved rim of the external ear.
-proper noun
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