A pointed or projecting end where two curves meet, especially on the crown of a tooth, the horns of a crescent moon, or the apex of an arch. The telescope clearly showed the bright cusps of the waxing crescent moon.
A pivotal or transitional point marking the threshold between two different states, stages, or conditions. The nation stood on the cusp of democratic reform.
Mathematics: a point on a curve where the curve changes direction abruptly and the tangent is undefined. At the cusp of the cycloid, the velocity of the rolling point momentarily drops to zero.
Astrology: the boundary between two zodiac signs or astrological houses. Born on the cusp of Aries and Taurus, he claimed to share traits of both signs.