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- Involute abstract "In the differential geometry of curves, an involute (also known as evolvent) is a curve obtained from another given curve by attaching an imaginary taut string to the given curve and tracing its free end as it is wound onto that given curve; or in reverse, unwound. It is a roulette wherein the rolling curve is a straight line containing the generating point. For example, an involute approximates the path followed by a tetherball as the connecting tether is wound around the center pole. If the center pole has a circular cross-section, then the curve is an involute of a circle.Alternatively, another way to construct the involute of a curve is to replace the taut string by a line segment that is tangent to the curve on one end, while the other end traces out the involute. The length of the line segment is changed by an amount equal to the arc length traversed by the tangent point as it moves along the curve.The evolute of an involute is the original curve, less portions of zero or undefined curvature. Compare Media:Evolute2.gif and Media:Involute.gifIf the function is a natural parametrization of the curve (i.e., for all s), then :parametrizes the involute.The notions of the involute and evolute of a curve were introduced by Christiaan Huygens in his work titled Horologium oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae (1673).".
- Involute wikiPageExternalLink 10.1007%2Fs12045-013-0106-3.
- Involute wikiPageExternalLink Involute.html.
- Involute wikiPageID "840704".
- Involute wikiPageRevisionID "586263290".
- Involute hasPhotoCollection Involute.
- Involute subject Category:Curves.
- Involute subject Category:Differential_geometry.
- Involute type Abstraction100002137.
- Involute type Attribute100024264.
- Involute type Curve113867641.
- Involute type Curves.
- Involute type Line113863771.
- Involute type Shape100027807.
- Involute comment "In the differential geometry of curves, an involute (also known as evolvent) is a curve obtained from another given curve by attaching an imaginary taut string to the given curve and tracing its free end as it is wound onto that given curve; or in reverse, unwound. It is a roulette wherein the rolling curve is a straight line containing the generating point. For example, an involute approximates the path followed by a tetherball as the connecting tether is wound around the center pole.".
- Involute label "Courbe développante".
- Involute label "Evolvente".
- Involute label "Evolvente".
- Involute label "Evolvente".
- Involute label "Evolvente".
- Involute label "Ewolwenta".
- Involute label "Involute".
- Involute label "Эвольвента".
- Involute label "伸開線".
- Involute label "漸伸線".
- Involute sameAs Evolventa.
- Involute sameAs Evolvente.
- Involute sameAs Evolvente.
- Involute sameAs Bilkari_(geometria).
- Involute sameAs Courbe_développante.
- Involute sameAs 伸開線.
- Involute sameAs 신개선.
- Involute sameAs Evolvente.
- Involute sameAs Ewolwenta.
- Involute sameAs Evolvente.
- Involute sameAs m.03g0x2.
- Involute sameAs Q680712.
- Involute sameAs Q680712.
- Involute sameAs Involute.
- Involute wasDerivedFrom Involute?oldid=586263290.
- Involute isPrimaryTopicOf Involute.
%20is%20a%20curve%20obtained%20from%20another%20given%20curve%20by%20attaching%20an%20imaginary%20taut%20string%20to%20the%20given%20curve%20and%20tracing%20its%20free%20end%20as%20it%20is%20wound%20onto%20that%20given%20curve%3B%20or%20in%20reverse%2C%20unwound.%20It%20is%20a%20roulette%20wherein%20the%20rolling%20curve%20is%20a%20straight%20line%20containing%20the%20generating%20point.%20For%20example%2C%20an%20involute%20approximates%20the%20path%20followed%20by%20a%20tetherball%20as%20the%20connecting%20tether%20is%20wound%20around%20the%20center%20pole.%20If%20the%20center%20pole%20has%20a%20circular%20cross-section%2C%20then%20the%20curve%20is%20an%20involute%20of%20a%20circle.Alternatively%2C%20another%20way%20to%20construct%20the%20involute%20of%20a%20curve%20is%20to%20replace%20the%20taut%20string%20by%20a%20line%20segment%20that%20is%20tangent%20to%20the%20curve%20on%20one%20end%2C%20while%20the%20other%20end%20traces%20out%20the%20involute.%20The%20length%20of%20the%20line%20segment%20is%20changed%20by%20an%20amount%20equal%20to%20the%20arc%20length%20traversed%20by%20the%20tangent%20point%20as%20it%20moves%20along%20the%20curve.The%20evolute%20of%20an%20involute%20is%20the%20original%20curve%2C%20less%20portions%20of%20zero%20or%20undefined%20curvature.%20Compare%20Media%3AEvolute2.gif%20and%20Media%3AInvolute.gifIf%20the%20function%20is%20a%20natural%20parametrization%20of%20the%20curve%20(i.e.%2C%20for%20all%20s)%2C%20then%20%3Aparametrizes%20the%20involute.The%20notions%20of%20the%20involute%20and%20evolute%20of%20a%20curve%20were%20introduced%20by%20Christiaan%20Huygens%20in%20his%20work%20titled%20Horologium%20oscillatorium%20sive%20de%20motu%20pendulorum%20ad%20horologia%20aptato%20demonstrationes%20geometricae%20(1673).%22%40en){kind=link}