cusp

English

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cusp

Wikipedia

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

cusp (plural cusps)

A sharp point or pointed end.
(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.
(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.
(architecture) A point made by the intersection of two curved lines or curved structures, a common motif in Gothic architecture.^[1]
(astrology) A boundary between zodiacal signs and houses.
(dentistry) Any of the pointed parts of a canine tooth or molar.
(anatomy) A flap of a valve of a heart or blood vessel.
A point of transition.
- 2021 October 20, Mark Rand, “S&C: a line fit for tourists... and everyone?”, in RAIL, number 942, page 40:
  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.

sharp point or pointed end

important moment when a decision is made

point of a curve where it has no tangent

in astrology

in dentistry

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

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