In mathematics, a dimension is the number of coordinates (or parameters) required to describe points of—or even points on—a mathematical object (usually geometric in nature). The dimension of an object is often referred to as its dimensionality. (For more about coordinates, see elsewhere in this chapter; for more about dimensions and science, see “Math in the Natural Sciences.”)

Each dimension represents points in space—from a single to multiple points. The concept of dimension is important in mathematics, as it defines a geometric object conceptually and/or visually. In fact, the idea of dimensions can even be applied to abstract objects that can’t be directly visualized. Mathematicians most often display such dimensions on graphs using a single point (for example, x) to represent one dimension; two points (usually x and y, or an ordered pair) to represent two dimensions; and three points (usually x, y, z) for three dimensions. The four- (and higher) dimensional analogs of three-dimensional objects often retain the prefix “hyper-” such as hypercube and hyperplane. The basic geometric structures of higher-dimensional geometry—the line, plane, space, and hyperspace—all consist of an infinite number of points arranged in specific ways.