tacnode

1. (geometry) A point of a curve where two or more osculating circles to the curve at that point are tangent, so that two branches of the curve have ordinary tangency at the double point.Examples: "A tacnode is defined to be a singularity equivalent to the origin in the curve y²-x²#61;0, that is, the union of two smooth arcs meeting with contact of order two. Similarly, an oscnode is a singularity equivalent to y²-x⁶#61;0, i.e., consisting of two smooth branched with contact of order three, and so on."