tacnode

English

The tacnode (at the origin) of the curve $(x^{2}+y^{2}-3x)^{2}-4x^{2}(2-x)=0$

Etymology

Latin tactus + English node

Noun

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^[1], page 262:

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

Related terms

• oscnode