oscnode
nounEtymology Blend of osculation + node.
1
Geometry, Mathematics, Sciences A node of a plane curve where two branches meet with contact order 3.
- Three nodes may coincide as consecutive points of a curve of finite curvature, giving rise, not to a triple point, but to the singularity called an oscnode; this is, in fact, an osculation or three-pointic contact of two branches of the curve.1879, George Salmon, A Treatise on the Higher Plane Curves, page 214:
- Rhamphoid cuspidal lines possess two kinds of singular points which affect the class of the surface, and occur (i) when the rhamphoid cusp changes into an oscnode, (ii) when there are cubic nodes on the surface.1908, A. B. Basset, “Singular liens and curves on surfaces”, in The Quarterly Journal of Pure and Applied Mathematics, volume 39, page 338:
1 more example
- 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.2012, Joe Harris, Algebraic Geometry: A First Course, page 262:
- Related terms
- tacnode