Tacnode

point of osculation, osculation point, double cusp

The third in the series of $A_k$-curve singularities. The point $(0,0)$ is a tacnode of the curve $X^4-Y^2=0$ in $\mathbf R^2$.

The first of the $A_k$-curve singularities are: an ordinary double point, also called a node or crunode; the cusp, or spinode; the tacnode; and the ramphoid cusp.

They are exemplified by the curves $X^{k+1}-Y^2=0$ for $k=1,2,3,4$.

The terms "crunode" and "spinode" are seldom used nowadays (2000).

See also Node; Cusp.

References[edit]