including Euclidean and Minkowski space. One of the most general types of mathe-
matical spaces is called the topological space.
How is a dimension describedin mathematics?
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 169
GEOMETRY AND TRIGONOMETRY
How do we interpret dimensions in everyday life?
W
e are all familiar with dimensions around us, although we may not be
aware of them. Most people are familiar with the ideas of two- (such as a
drawing on paper) and three-dimensional objects (ordinary objects, including an
apple or a car, exist in three-dimensional space), but there are others as well.Zero dimension can be thought of as a point in space. One dimension can be
visualized by a line or a curve in space. Another way of understanding one
dimension is with time, something we think of as consisting of only “now,”
“before,” and “after.” Because the “before” and “after”—regardless of whether
they are long or short—are actually extensions, time becomes similar to a line
(as in “timeline”)—or a one-dimensional object.Two dimensions are defined by two coordinates in space, such as a rectangle.
One of the most obvious two-dimensional objects we see all around us are paint-
ings and photographs—although they represent a three-dimensional object.
Even this page you are reading can be considered a two-dimensional object,
though strictly speaking, the thickness of the paper gives it a third dimension.
Three dimensions are considered the space we occupy, as three dimensions gives
everything around us depth. Our binocular vision allows us to see depth (things
in three dimensions), which is why everything becomes “flat” or two-dimension-
al when we view the world through just one eye.
One can also conceive of four or more dimensions, but there are few com-
mon examples. Most hyper-dimensional aspects are used by mathematicians,
various scientists, and even economists. They need such dimensional analysis for
their complex mathematics, such as for modeling weather patterns or the ups
and downs of the stock market.