A plane curve is a curve that lies in a single plane. A plane curve may be closed or open. Curves which are interesting for some reason and whose properties have therefore been investigates are called "special" curves (Lawrence 1972). Some of the most common open curves are the line, parabola, and hyperbola, and some of the most common closed curves are the circle and ellipse.
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.Plane curves also include the Jordan curves (curves that enclose a region of the plane but need not be smooth) and the graphs of continuous functions.
Numerous examples of plane curves are shown in Gallery of curves and listed at List of curves. The algebraic curves of degree 1 or 2 are shown here (an algebraic curve of degree less than 3 is always contained in a plane):
Of the various systems for representing plane curves,* six will be discussed in this section. Each system has its own advantages and difficulties, as indicated in Table 1. Most of the succeeding chapters will use the parametric representation within a Cartesian coordinate system; direct Cartesian representation and polar representation will occur somewhat less frequently; and pedal, bipolar, and intrinsic systems will be of infrequent use. 2b1af7f3a8