What is "plane curve"

Plane \Plane\, a. [L. planus: cf. F. plan. See Plan, a.] Without elevations or depressions; even; level; flat; lying in, or constituting, a plane; as, a plane surface.

Note: In science, this word (instead of plain) is almost exclusively used to designate a flat or level surface.

Plane angle, the angle included between two straight lines in a plane.

Plane chart, Plane curve. See under Chart and Curve.

Plane figure, a figure all points of which lie in the same plane. If bounded by straight lines it is a rectilinear plane figure, if by curved lines it is a curvilinear plane figure.

Plane geometry, that part of geometry which treats of the relations and properties of plane figures.

Plane problem, a problem which can be solved geometrically by the aid of the right line and circle only.

Plane sailing (Naut.), the method of computing a ship's place and course on the supposition that the earth's surface is a plane.

Plane scale (Naut.), a scale for the use of navigators, on which are graduated chords, sines, tangents, secants, rhumbs, geographical miles, etc.

Plane surveying, surveying in which the curvature of the earth is disregarded; ordinary field and topographical surveying of tracts of moderate extent.

Plane table, an instrument used for plotting the lines of a survey on paper in the field.

Plane trigonometry, the branch of trigonometry in which its principles are applied to plane triangles.

Curve \Curve\, n. [See Curve, a., Cirb.]

1. A bending without angles; that which is bent; a flexure; as, a curve in a railway or canal.

2. (Geom.) A line described according to some low, and having no finite portion of it a straight line.

   Axis of a curve. See under Axis.

   Curve of quickest descent. See Brachystochrone.

   Curve tracing (Math.), the process of determining the shape, location, singular points, and other peculiarities of a curve from its equation.

   Plane curve (Geom.), a curve such that when a plane passes through three points of the curve, it passes through all the other points of the curve. Any other curve is called a curve of double curvature, or a twisted curve.

n. (context mathematics English) the locus of points in the Euclidean plane that satisfies some geometric or algebraic definition

In mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves.