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A helix (pl: helixes or helices) 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 ramp – is called a helicoid. 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".〔(ἕλιξ ), Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus〕 ==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 width 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.〔"(Double Helix )" by Sándor Kabai, Wolfram Demonstrations Project.〕 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〔O'Neill, B. ''Elementary Differential Geometry,'' 1961 pg 72〕 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.〔O'Neill, B. ''Elementary Differential Geometry,'' 1961 pg 74〕 A curve is called a slant helix if its principal normal makes a constant angle with a fixed line in space.〔Izumiya, S. and Takeuchi, N. (2004) ''New special curves and developable surfaces.'' (Turk J Math ), 28:153–163.〕 It can be constructed by applying a transformation to the moving frame of a general helix.〔Menninger, T. (2013), ''An Explicit Parametrization of the Frenet Apparatus of the Slant Helix''. (arXiv:1302.3175 ).〕 Some curves found in nature consist of multiple helices of different handedness joined together by transitions known as tendril perversions. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「helix」の詳細全文を読む スポンサード リンク
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