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A curve with a cusp at (0,0)
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From Latin cuspis (a point, spear, pointed end); first used in astrology.


  • IPA(key): /kʌsp/
  • (file)
  • Rhymes: -ʌsp


cusp (plural cusps)

  1. A sharp point or pointed end.
  2. (figuratively) An important moment when a decision is made that will determine future events.
    • 2012 April 21, Jonathan Jurejko, “Newcastle 3-0 Stoke”, in BBC Sport[1]:
      Newcastle were 11 points adrift of Spurs following their 5-0 mauling at the hands of the north London club in February.
      But a sixth successive Premier League win puts them on the cusp of European football next season as they surged 15 points clear of seventh-placed Everton, who have five games left to play.
  3. (geometry) A point of a curve where the curve is continuous but has no derivative, but such that it has a derivative at every nearby point.
  4. (architecture) A point made by the intersection of two curved lines or curved structures, a common motif in Gothic architecture.[1]
  5. (astrology) A boundary between zodiacal signs and houses.
  6. (dentistry) Any of the pointed parts of a canine tooth or molar.
  7. (anatomy) A flap of a valve of a heart or blood vessel.


  • (sharp point, pointed end): ord

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cusp (third-person singular simple present cusps, present participle cusping, simple past and past participle cusped)

  1. (slang) To behave in a reckless or dangerous manner.


  1. ^ Russell Sturgis, ed. (1902). A Dictionary of Architecture and Building: Biographical, Historical, and Descriptive. 3. Macmillan.