# Generatrix

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Geometric object moved along a path to generate a shape

Look up ***[generatrix](https://en.wiktionary.org/wiki/generatrix)*** in Wiktionary, the free dictionary.

In [geometry](/source/Geometry), a **generatrix** ([/dʒɛnəˈreɪtrɪks/](https://en.wikipedia.org/wiki/Help:IPA/English)) or **describent** is a [point](/source/Point_(geometry)), [curve](/source/Curve) or [surface](/source/Surface_(mathematics)) that, when moved along a given path, generates a new [shape](/source/Shape).[1] The path directing the motion of the generatrix motion is called a **directrix** or **dirigent**.[2]

## Examples

A [cone](/source/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](/source/Rotation_around_a_fixed_axis) and the resulting shape is a circular cone.[3]

The generatrix of a [cylinder](/source/Cylinder_(geometry)), a limiting case of a cone, is a line that is kept [parallel](/source/Parallel_(geometry)) to some axis.

## See also

- [Surface of revolution](/source/Surface_of_revolution)

## References

1. **[^](#cite_ref-1)** ["generatrix"](https://www.merriam-webster.com/dictionary/generatrix). *merriam-webster.com*. Retrieved 11 September 2014.

1. **[^](#cite_ref-2)** ["generatrix"](https://www.mathopenref.com/generatrix.html). *mathopenref.com*. Retrieved 11 September 2014.

1. **[^](#cite_ref-3)** ["Cone"](https://www.britannica.com/science/cone-mathematics). *britannica.com*. Retrieved 11 September 2014.

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