Plane Curve


Also found in: Dictionary, Wikipedia.

plane curve

[′plān ‚kərv]
(mathematics)
Any curve lying entirely within a plane.

Plane Curve

 

a curve whose points are all coplanar. It can be defined analytically by means of Cartesian or polar coordinates. In Cartesian coordinates it can be given in implicit form, F(x, y) = 0; in explicit form, y = f(x); or in parametric representation, x = ɸ(t) and y = ψ(t). The polar representation is ρ = f(ɸ).

References in periodicals archive ?
In this short note we want to compare two approaches to compute the Euler characteristic of the Milnor fibre of a plane curve singularity.
iii) If q = 0, then c [is less than or equal to] 5 and c = 5 precisely when C is a plane curve of degree 9.
Since C is smooth, we see that C is isomorphic to a plane curve of degree [greater than or equal to] 8, contradicting the assumption g [less than or equal to] 3.
Oka, On the fundamental group of the complement of certain plane curves, J.
For any irreducible plane curve C = {F = 0} whose only singularities are nodes and cusps, the set of quasitoric relations of C {(f, g, h) [member of] C[[x, y, z].
2]) the real plane curve obtained by this net has only points of multiplicity at most 2.
In this article, we continue to study Zariski pairs for reducible plane curves based on the idea used in [3].
Ito traces the development of current methods in knot projections, a branch of topology, based on research inspired by Arnold's theory of plane curves, Viro's quantization of the Arnold invariant, Vasseliev's theory of knots, and other findings.
A few years ago, on a crisp autumn day in Cambridge Massachusetts, I attended a lecture entitled Singularities in Algebraic Plane Curves.
This edition integrates innovations during the past decade, primarily in twisted polynomial invariants, singularities of plane curves, knot modules, and nilpotent quotients.
Study some conjectures on rational cuspidal plane curves, Q-acyclic open surfaces and normal surface singulatities with rational homology sphere links, via algebra-geometric and topological techniques.