# cusp

In mathematics, a cusp is a point on a curve where two branches, coming from different
directions, meet and have a common tangent.
If the two branches of the curve approach the tangent from opposite sides
the cusp is called a **keratoid** (from the Greek *kera* for horn) or **first-order cusp**. This is the case, for example,
with the curve given by the equation *y*^{2} = *x*^{2}*y* + *x*^{5}. If the two branches of the curve approach the
tangent from the same side the result is a **ramphoid** or **second-order cusp**. The curvature at a cusp is infinite.

"Cusp" derives from the Latin *cuspis* for sharp. Outside of mathematics, the points of a crescent moon are called
cusps and the sharp pointed premolar teeth of children are known as bicuspids.