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Generalized helicoid
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Generalized helicoid : ウィキペディア英語版
Generalized helicoid

In geometry, a generalized helicoid is a surface in Euclidean space generated by rotating and simultaneously displacing a curve, the ''profile curve'', along a line, its ''axis''. Any point of the given curve is the starting point of a circular helix. If the profile curve is contained in a plane through the axis, it is called the meridian of the generalized helicoid. Simple examples of generalized helicoids are the helicoids. The meridian of a helicoid is a line which intersects the axis orthogonally.
Essential types of generalized helicoids are
* ruled generalized helicoids. Their profile curves are lines and the surfaces are ruled surfaces.
*circular generalized helicoids. Their profile curves are circles.
In mathematics helicoids play an essential role as minimal surfaces.
In the technical area generalized helicoids are used for staircases, slides, skrews and pipes.
== Analytical representation ==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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