glissette

{{Short description|Curve traced by another curve that slides along two fixed curves}}

In geometry, a glissette is a curve determined by either the locus of any point, or the envelope of any line or curve, that is attached to a curve that slides against or along two other fixed curves.

Examples

=Ellipse=

A basic example is that of a line segment of which the endpoints slide along two perpendicular lines. The glissette of any point on the line forms an ellipse.{{cite book|last1=Besant|first1=William|title=Notes on Roulettes and Glissettes|date=1890|publisher=Deighton, Bell|page=51|url=https://archive.org/details/notesonroulette00besagoog|accessdate=6 April 2017}}

File:Glissette_ellipse.gif

=Astroid=

Similarly, the envelope glissette of the line segment in the example above is an astroid.{{cite book|last1=Yates|first1=Robert C.|title=A Handbook on Curves and their Properties|date=1947|publisher=Edwards Bros.|location=Ann Arbor, MI|page=109|url=https://archive.org/details/YatesHandbookCurves1947|accessdate=6 April 2017}}

File:Astroid_glissette.png

=Conchoid=

Any conchoid may be regarded as a glissette, with a line and one of its points sliding along a given line and fixed point.{{cite book|last1=Lockwood|first1=E. H.|title=A Book of Curves|date=1961|publisher=Cambridge University Press|page=162|url=http://www.aproged.pt/biblioteca/ABookofCurvesLockwood.pdf|accessdate=6 April 2017|archive-date=21 February 2017|archive-url=https://web.archive.org/web/20170221212535/http://www.aproged.pt/biblioteca/ABookofCurvesLockwood.pdf|url-status=live}}

File:Nicomedes.gif

References

External links

[http://mathworld.wolfram.com/Glissette.html Glissette at Wolfram Mathworld] {{Webarchive|url=https://web.archive.org/web/20170421065745/http://mathworld.wolfram.com/Glissette.html |date=2017-04-21 }}

Category:Curves