So far we have dealt with points, lines, and planes. All of these
lie within space. Space is the collection of all points. It has no shape,
and it has no limits. Space is three-dimensional; that is, it has length,
width, and a new dimension, height. Again, height is only length in a different
direction. Height is a measurement of length perpendicular to length and
width. Imagine a box: It has length, width, and height. It encloses space.
A region in space can be either zero, one, two, or three-dimensional. A
zero-dimensional region in space is a point. Instead of calling a point a region,
because it is spanned by zero lines, it is more understandable to call it a
location. Lines and planes are also regions in space. A three-dimensional
object, like a ball of clay or a raindrop, also occupies a region in space. So
does your shoe, your house, and your finger. Each is a collection of points.
These four building blocks of geometry, points, lines, planes, and space, form
the basis for all of the geometry you will study in this guide. It is important
to understand their properties fully. Depictions of points, lines, and planes
on paper (or computer screens) often are misleading because they appear to add
dimensions to the basic building blocks. Points appear to have dimension, lines
appear to have width, and planes appear to have thickness. It is critically
important to remember now and forever the true nature of these basic elements of
geometry, so that they don't mislead you in the future when things are much more
difficult to visualize.