Definition

1. Adjective:
   • Having cusps or points: Describes a shape, curve, or structure that features one or more sharp, pointed projections or tips. In mathematics, it often refers to a singular point on a curve where the tangent direction is undefined.

Examples of Usage

• Adjective:
  • The cuspidal shape of the mountain peak was visible against the sky.
  • In algebraic geometry, the curve has a cuspidal singularity at the origin.

Advanced Usage

• Cuspidal representation: In advanced mathematics, particularly in the theory of automorphic forms, this term refers to a specific type of representation with particular vanishing properties.

  • The theory focuses on the decomposition of the spectrum into discrete series and cuspidal representations.

• Cuspidal edge: In differential geometry, this is a type of singularity on a surface.

  • The surface develops a cuspidal edge along that parameter line.

Variants and Related Words

• Cusp (n): A point or pointed end, especially where two curves meet. The fundamental noun from which 'cuspidal' is derived.

  • The cusp of a tooth; the cusp of a crescent moon.

• Cuspidate (adj): Another adjective meaning having a cusp or cusps; pointed.

  • The leaf has a cuspidate tip.

Synonyms

• Pointed: Having a sharp tip or end.
• Acuminate: Tapering to a slender point (often used in biology for leaves).

Antonyms

• Blunt: Having a worn or rounded edge, not sharp.
• Rounded: Having a smooth, curved shape without points.

Adjective

1. having cusps or points