Dimension is a characteristic of all geometric regions, objects, and spaces.
The previous sections have probably already made you aware of the concept of
dimension. It is roughly the number of directions in which a region or object
can be measured. More formally, it is the number of lines required to span
a region in space. Examples make dimension much easier to understand.

A point is zero-dimensional. It has no length, width, thickness, or any
other physical means of measurement. It only exists as a symbol to identify a
single location in space.

A line is one-dimensional. It has the dimension of length. To put it another
way, there is only one way that you can move along a line: lengthwise. In a
similar vein, there is no way to move within a point. A point is a single
location in itself, whereas a line is a collection of points, or locations.

A plane is two-dimensional. It has length and width. (Technically
speaking, the property of width is really only length in a different direction).
You can move along a plane in two directions, lengthwise and widthwise. You
might think that you can actually move along a plane in an infinite number of
directions, but actually every direction in which you move can be broken down
into a component of length and a component of width.

It should now be easier to understand the more formal definition of dimension:
the number of lines required to span a region in space:

A point is not a region in space, it is only a specific location.
Therefore it takes zero lines to span it, and it is zero-dimensional.

One line is required to span a line (itself). Therefore a line is one-
dimensional.

It requires two lines to span a plane, so therefore a plane is two-
dimensional. These two lines represent length and width. Any point in the
plane can be expressed as a combination of a certain length and a certain
width, depending on the location of the point. The span of a line (or many
lines) is the region that contains all the points that can be expressed as
combinations of that line (or lines). A geometric space can also be spanned by
points or planes.