A curve is representative of a line which is not straight. A curve begins and finishes similar to a line, but stops resembling a straight line as it approaches the formation of its bulge or deformation. For instance, a parabola is an example of a curve.
Figure 1. This illustration is representative of a curve. As is depicted in this figure, a curve bulges outwards near the middle.
Curves are generally thought to be plane curves and are therefore two dimensional. However, in some cases curves can be three dimensional. These types of curves are referred to as space curves.
In the study of geometry, curves are particularly important to the areas of differential geometry and algebraic geometry. In differential geometry, a curve is referenced as a differentiable curve and this curve does not exist in two dimensional space.
In algebraic geometry, curves are known as algebraic curves and can be either plane curves, space curves or of a higher dimension. For example, an elliptic curve, which is studied in number theory, is an example of an algebraic curve.