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cusp

noun

  1. point on a curve where a moving point on the curve must start to move backward
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Wiktionary

Pronunciation: /kʌsp/ / /kʊsp/

noun

Etymology: From Latin cuspis (“a point, spear, pointed end”); first used in astrology. Doublet of cuspid and cuspis.

  1. A sharp point or pointed end.
  2. An important moment when a decision is made that will determine future events.

    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. 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. A point made by the intersection of two curved lines or curved structures, a common motif in Gothic architecture.
  5. A boundary between zodiacal signs and houses.
  6. Any of the pointed parts of a canine tooth or molar.
  7. A flap of a valve of a heart or blood vessel.
  8. A point of transition.

    I see freight returning in a big way. The 2016 reconnection of the Helwith Bridge quarries can produce up to three heavy trains a day. The nearby and much bigger Horton quarry is also on the cusp of rail reconnection.

verb

Etymology: From Latin cuspis (“a point, spear, pointed end”); first used in astrology. Doublet of cuspid and cuspis.

  1. To behave in a reckless or dangerous manner.