cusp

plural cusps

1. A sharp point or pointed end.

   Synonyms: ord

2. figurativelyAn important moment when a decision is made that will determine future events.

   1 more example

   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.

   2012 April 21, Jonathan Jurejko, “Newcastle 3-0 Stoke”, in BBC Sport

3. geometryA 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. architectureA point made by the intersection of two curved lines or curved structures, a common motif in Gothic architecture.
5. astrologyA boundary between zodiacal signs and houses.
6. dentistryAny of the pointed parts of a canine tooth or molar.
7. anatomyA 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.

   2021 October 20, Mark Rand, “S&C: a line fit for tourists... and everyone?”, in RAIL, number 942, page 40

present singular third person cusps · participle present cusping · participle past cusped · past cusped

1. slangTo behave in a reckless or dangerous manner.