Editing Involute (section)

{{short description|Curve traced by a string as it is unwrapped from another curve}}
[[File:Evolvente-parabel.svg|thumb|Two involutes (red) of a parabola]]
{{distinguish|involution (mathematics)}}
In [[mathematics]], an '''involute''' (also known as an '''evolvent''') is a particular type of [[curve]] that is dependent on another shape or curve. An involute of a curve is the [[Locus (mathematics)|locus]] of a point on a piece of taut string as the string is either unwrapped from or wrapped around the curve.<ref>{{Cite book|title=Geometry of Curves|last=Rutter|first=J.W.|publisher=CRC Press|year=2000|isbn=9781584881667|pages=[https://archive.org/details/geometryofcurves0000rutt/page/204 204]|url=https://archive.org/details/geometryofcurves0000rutt/page/204}}</ref>

The [[evolute]] of an involute is the original curve.

It is generalized by the [[Roulette (curve)|roulette]] family of curves. That is, the involutes of a curve are the roulettes of the curve generated by a straight line.

The notions of the involute and evolute of a curve were introduced by [[Christiaan Huygens]] in his work titled ''[[Horologium Oscillatorium|Horologium oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae]]'' (1673), where he showed that the involute of a cycloid is still a cycloid, thus providing a method for constructing the [[cycloidal pendulum]], which has the useful property that its period is independent of the amplitude of oscillation.<ref>{{Cite book|title=Geometry from a Differentiable Viewpoint|url=https://archive.org/details/geometryfromdiff00mccl_866|url-access=limited|last=McCleary|first=John|publisher=Cambridge University Press|year=2013|isbn=9780521116077|pages=[https://archive.org/details/geometryfromdiff00mccl_866/page/n105 89]}}</ref>