# Plane Curve

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## plane curve

[′plān ‚kərv]
(mathematics)
Any curve lying entirely within a plane.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## 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 ?
Let C [subset] [P.sup.2] be a smooth plane curve of degree d (d [greater than or equal to] 4) and C(C) the function field of C.
On the other hand, the profiles of plane curves or intersurface attracted more and more attention.
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.
In this article, we continue to study Zariski pairs for reducible plane curves based on the idea used in .
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.
Theorem 8 Let [x(s), y(s)] be a regular parametric plane curve of class [C.sub.3], and P be a point which is not a point of [x(s), y(s)], and the tangents of [x(s), y(s)] do not pass through P.
Other topics include conjugate vectors of immersed manifolds, Thom polynomials and Schur functions, obstructions on fundamental groups of plane curve complements, and exotic moduli of Goursat distributions.
Fundamental groups of plane curve complements play an important role in the study of branched coverings.
has no [g.sup.1.sub.2]) the real plane curve obtained by this net has only points of multiplicity at most 2.

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