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Helix

A helix , from the Greek word ????a?/????, is a twisted shape like a spring, screw Screw

... 

 or a spiral Spiral

In mathematics [i], a spiral is a curve [i] which emanates from a central point, getting progressively f ... 

 staircase. Helices are important in biology Biology

Biology is the branch of science [i] dealing with the study of life [i]. ... 

, as DNA DNA

Deoxyribonucleic acid is a nucleic acid [i] that contains the genetic [i] instructions for t ... 

 is helical and many protein Protein

Proteins are large organic compound [i]s made of amino acid [i]s arranged in a linear chain and joined b ... 

s have helical substructures, known as alpha helices Alpha helix

A common motif in the secondary structure [i] of protein [i]s, the alpha helix is ... 

. 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.

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Encyclopedia

A helix , from the Greek word ????a?/????, is a twisted shape like a spring, screw Screw

... 

 or a spiral Spiral

In mathematics [i], a spiral is a curve [i] which emanates from a central point, getting progressively f ... 

 staircase. Helices are important in biology Biology

Biology is the branch of science [i] dealing with the study of life [i]. ... 

, as DNA DNA

Deoxyribonucleic acid is a nucleic acid [i] that contains the genetic [i] instructions for t... 

 is helical and many protein Protein

Proteins are large organic compound [i]s made of amino acid [i]s arranged in a linear chain and joined b ... 

s have helical substructures, known as alpha helices Alpha helix

A common motif in the secondary structure [i] of protein [i]s, the alpha helix is
... 

.


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 Mathematics

Mathematics is the discipline that deals with concepts such as quantity [i], structure [i], space [i] a ... 

, a helix is a curve in 3-dimension Dimension

In common usage, a dimension is a parameter [i] or measurement [i] required to define the characteristi ... 

al space. The following three equations in rectangular coordinates Cartesian coordinate system

In mathematics [i], the Cartesian coordinate system is used to uniquely determine each point [i]... 

 define a helix:

x = cos Trigonometric function

In mathematics [i], the trigonometric functions are function [i]s of an angle [i]; they are im ... 

y = sin Trigonometric function

In mathematics [i], the trigonometric functions are function [i]s of an angle [i]; they are im ... 

z = t


Here t is a real parameter Parameter

In mathematics [i], statistics [i], and the mathematical science [i]s, parameters are quantities that d ... 

. As t increases, the point traces a right-handed helix of pitch 2p Pi

The mathematical constant [i] p is an irrational [i] real number [i], approximately eq ... 

 about the z-axis, in a right-handed coordinate system.

In cylindrical coordinates Cylindrical coordinate system

The cylindrical coordinate system is a three-dimensional coordinate system [i] which essentially extends ... 

 , the same helix is described by:
r = 1
? = h


Except for rotation Rotation

Rotation is the movement of an object in a circular motion.... 

s, translation Translation

Translation is an activity comprising the interpretation [i] of the meaning [i] of a text in on ... 

s, 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 Double helix

In geometry [i] a double helix typically consists of two congruent helices [i] with the same axis, ... 

 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 Music

Music is an art, entertainment [i], or other human activity that involves organized and audible sounds a ... 

, pitch space is often modeled with helices or double helices, most often extending out of a circle such as the circle of fifths Circle of fifths

In music theory [i], the circle of fifths is a geometrical space that depicts relationships among the 12 ... 

, so as to represent octave equivalency.


A conic helix may be defined as a spiral Spiral

In mathematics [i], a spiral is a curve [i] which emanates from a central point, getting progressively f ... 

 on a conic surface, with the distance to the apex an exponential function of the angle indicating direction from the axis.

See also

  • DNA DNA

    Deoxyribonucleic acid is a nucleic acid [i] that contains the genetic [i] instructions for t... 

  • Collagen Collagen

    Collagen is the main protein [i] of connective tissue [i] in animal [i]s and the most abundant protein i ... 





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