tacnode

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tacnode

Wikipedia

Latin tactus + English node

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tacnode (plural tacnodes)

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.
   • 2012, Joe Harris, Algebraic Geometry: A First Course‎, page 262:

     A tacnode is defined to be a singularity equivalent to the origin in the curve ${\displaystyle y^{2}-x^{2}=0}$, that is, the union of two smooth arcs meeting with contact of order two. Similarly, an oscnode is a singularity equivalent to ${\displaystyle y^{2}-x^{6}=0}$, i.e., consisting of two smooth branched with contact of order three, and so on.

• oscnode