Flecnode

on a planar curve

A point at which a node (or double point; cf. also Node) and an inflection (cf. also Point of inflection) coincide.

Thus, one of the tangents at the node has intersection multiplicity at least $4$ with the curve at that point.

References

[a1]	J.W. Bruce, "Lines, surfaces and duality" Math. Proc. Cambridge Philos. Soc. , 112 (1992) pp. 53–61
[a2]	M. Tsuboko, "On the line complex determinant of flecnode tangents of a ruled surface and its flecnodal surfaces" Memoirs Ryojun Coll. Engin. , 11 (1938) pp. 233–238