Generatrix
{{short description|Geometric object moved along a path to generate a shape}}
{{wiktionary|generatrix}}
In geometry, a generatrix ({{IPAc-en|dʒ|ɛ|n|ə|'|r|eɪ|t|r|ɪ|k|s}}) or describent is a point, curve or surface that, when moved along a given path, generates a new shape.{{cite web|title=generatrix|url=https://www.merriam-webster.com/dictionary/generatrix|website=merriam-webster.com|accessdate=11 September 2014}} The path directing the motion of the generatrix motion is called a directrix or dirigent.{{cite web|title=generatrix|url=https://www.mathopenref.com/generatrix.html|website=mathopenref.com|accessdate=11 September 2014}}
Examples
A cone can be generated by moving a line (the generatrix) fixed at the future apex of the cone along a closed curve (the directrix); if that directrix is a circle perpendicular to the line connecting its center to the apex, the motion is rotation around a fixed axis and the resulting shape is a circular cone.{{cite web|title=Cone|url=https://www.britannica.com/science/cone-mathematics|website=britannica.com|accessdate=11 September 2014}}
The generatrix of a cylinder, a limiting case of a cone, is a line that is kept parallel to some axis.