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Generatrix

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In geometry, a generatrix (/dʒɛnəˈreɪtrɪks/) or generator is a point, curve or surface that, when moved along a given path, generates a new shape.[1] The path directing the motion of the generatrix motion is called a directrix.[2]

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.[3]

The generatrix of a cylinder, a limiting case of a cone, is a line that is kept parallel to some axis.

References

  1. ^ "generatrix". merriam-webster.com. Retrieved 11 September 2014.
  2. ^ "generatrix". mathopenref.com. Retrieved 11 September 2014.
  3. ^ "Cone". britannica.com. Retrieved 11 September 2014.
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