cusp

A curve with a cusp at (0,0)

Meaning

A sharp point or pointed end.
An important moment when a decision is made that will determine future events.
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.
A point made by the intersection of two curved lines or curved structures, a common motif in Gothic architecture.
A boundary between zodiacal signs and houses.
Any of the pointed parts of a canine tooth or molar.
A flap of a valve of a heart or blood vessel.
A point of transition.

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