Cusp (singularity)

Common card · No. 474940

In mathematics, a cusp, sometimes called spinode in old texts, is a point on a curve where a moving point must reverse direction. A typical example is given in the figure. A cusp is thus a type of singular point of a curve. For a plane curve defined by an analytic, parametric equation x = f ( t ) y = g ( t ) , {\displaystyle {\begin{aligned}x&=f(t)\\y&=g(t),\end{aligned}}} a cusp is a point where both derivatives of f and g are zero, and the directional derivative, in the direction of the tangent, changes...

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