Lines are two-dimensional objects defined by two or more distinct points. In mathematics, there are two types of lines: straight lines and curved lines. While a straight line segment will always have a slope that is constant, the slope of a curved line segment will be different at each point along the line.
Closed Curves
A closed curve is a mathematical term that refers to a shape with no endpoints. A closed curve can be simple, meaning that the curve never crosses over itself. Examples of simple closed curves include circles, ovals and polygons. A non-simple or complex closed curve is a curve in which segments of the curve cross over each other such as in a figure eight. Although the term curve is used, a closed curve does not need to contain any curved lines. It can contain curved lines, straight lines or a combination of both. A simple or a non-simple closed curve does not need to be a regular or uniform shape; a flower outline, an irregular blob outline or an arrow outline are all examples of closed curves.
Open Curves
As its name would suggest, an open curve is any curve where the endpoints don't meet. The letter U is an example of an open curve. As with closed curves, open curves can be composed of either straight or curved lines or a combination of both. Open curves can be irregular or regular shapes. Also like closed curves, an open curve is considered simple if its segments never cross.
Bezier Curves
A Bezier curve is a type of open curve used in many computer drawing and design programs. This classical curve is named for Pierre Bezier who introduced the curves for use with computer-assisted design software. Although a Bezier curve is a line segment, it is defined by not two, but four separate points. Although it can't be seen, these four points form a quadrilateral shape that contains the curve. Moving any of these points will change the shape of the Bezier curve.
Parabolas
A parabola is another type of simple open curve. One way to picture a parabola is as an ellipse with one focus in infinity. It is a uniform curve in which the two sides expand outward from the focus infinitely. The parabola is a type of curve that lends itself to shapes like satellite dishes and suspension bridges.