Main > Curves and Surfaces > Curves
Maps from R1 into R2 or R3.
 Types of Curves Ways of defining and classifying curves. Common Curves Curves that occur frequently in mathematics at all levels. Special Curves Curves with particularly interesting properties. Miscellaneous Curves Assorted less common curves.

We all have an intuitive idea of what curves are. A length of string lying on a table and a piece of wire bent in space both trace curves. So does the graph of a function y = f(x), or the boundary of a region like a disk. But while we may have a very good sense of what a curve is, we need a mathematically precise definition from which we can proceed to discuss different varieties of curves with different properties. A good working definition is that a curve is a map from R1 into Rn. That is, a curve is a function which takes a single number as its input and returns a vector. In the case where n = 2, we call the curve a plane curve. When n = 3, we call the curve a space curve. The above topics divide up the many curves in the library into classes.