One of the most misunderstood concepts in mathematics, dimension is a central concept in modern geometry, topology, algebra, and the theory of fractals. To make matters even more complicated, each of these branches of mathematics has its own version of dimension (or even several versions).

In simplest terms, the dimension of a mathematical object is the number of independent parameters required to describe that object. It is well known that the dimension of a line is 1, the dimension of a plane is 2, and the dimension of space is 3. For example, any point in space can be described by three coordinates; a box in space is described by three parameters, its height, width and depth.

However, most people have difficulty imagining dimensions larger than 3; it is sometimes asserted that "The fourth dimension is time." As a statement about our physical universe, this may be correct; as a mathematical statement...