cusp

Concise Oxford English Dictionary © 2008 Oxford University Press:
cusp /kʌsp/

▶noun

• 1 a pointed end where two curves meet.

  ■ each of the pointed ends of the crescent moon.

  ■ a cone-shaped prominence on the surface of a tooth.

  ■ Architecture a projecting point between small arcs in Gothic tracery.

• 2 Mathematics a point at which the direction of a curve is abruptly reversed.

• 3 Astrology the initial point of an astrological sign or house.

  ■ a point of transition between two different states: those on the cusp of adulthood.

• 4 Anatomy a pocket or fold in the wall of the heart or a major blood vessel, forming part of a valve.

– derivatives
cuspate adjective,
cusped adjective,
cusping noun.

– origin C16: from L. cuspis ‘point or apex’.