generatrices

A cone is formed by rotating a triangle around one of its generatrices.

Definition

1. Noun (plural form of ):
   • Mathematics (Geometry): In geometry, "generatrices" are the plural of "generatrix," which refers to a point, line, or curve that, when moved along a given path (the directrix), generates a surface. Specifically, it is the moving element that traces out a surface, such as a line that sweeps to form a cylinder or cone.

Usage Examples

• (The moving lines that form the cone's surface.)
• (The lines that sweep to create the cylindrical shape.)
• (The individual lines that make up the surface.)

Advanced Usage

• "Generatrix" (singular) is a technical term in differential geometry and descriptive geometry. The plural "generatrices" is used when referring to multiple such lines or curves.
  • The helicoid is a ruled surface where generatrices twist around a central axis. (The lines that form the twisted surface.)

Variants and Related Words

• Generatrix (noun, singular): a single moving line or curve that generates a surface.

  • The generatrix of a cone is a straight line through the vertex. (The line that sweeps to form the cone.)

• Generator (noun): in mathematics, a broader term for an element that generates a set or structure (e.g., a generator of a group).

  • The generator of a cyclic group is an element that can produce all other elements. (A related but distinct concept.)

Synonyms

• Directrix (related but opposite): The fixed curve or line that guides the generatrix in generating a surface.

  • The directrix is the path along which the generatrix moves. (A complementary term in surface generation.)

• Ruling line: In the context of ruled surfaces, a synonym for a generatrix.

  • Each ruling line on a hyperboloid is a generatrix. (A straight line on a doubly ruled surface.)

Related Idioms

• "To generate a surface": a mathematical phrase meaning to create a surface by moving a generatrix along a directrix.

  • By rotating the generatrix around an axis, we generate a surface of revolution. (The process of surface creation.)

• "Ruled surface": a surface that can be formed by moving a straight line (a generatrix) along a curve.

  • A cylinder is a simple ruled surface with parallel generatrices. (A surface composed entirely of straight lines.)