Hausdorff Dimension
In everyday life, we usually think about the whole-number topological dimensions of smooth objects. For example, a place is two-dimensional because a point on a plane can be described by two independent parameters, for example, locations along an x- and yaxis. A straight line is one dimensional.
For certain more complicated sets and curves, the Hausdorff dimension provides another way to define dimension. For example, imagine a line that zig zags and twists in such an intricate way that it partially fills the plane. Its Hausdorff increases beyond 1 and takes on values that get closer and closer to 2 the more the line fills the plane.
