tacnode

English

The tacnode (at the origin) of the curve

{\\displaystyle (x^{2}+y^{2}-3x)^{2}-4x^{2}(2-x)=0}

Latin tactus + English node

tacnode (plural tacnodes)

(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.

单词	tacnode
释义	tacnode English The tacnode (at the origin) of the curve ${\\displaystyle (x^{2}+y^{2}-3x)^{2}-4x^{2}(2-x)=0}$ Etymology Latin tactus + English node Noun tacnode (plural tacnodes) (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. Related terms oscnode
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