Mapmaking - The Science of Navigation - page 97

FIGURE 4.4. Unprojected, or plate carrée , map of the world. Distances, angles, and
areas are all distorted. Such a map is easy to draw, however, because the x -axis (hori-
zontal axis) of the map is just longitude, while the y -axis (vertical axis) is latitude.
Thus, parallels are horizontal and equally spaced, and meridians are vertical and
equally spaced. NASA image.
It is impossible for a map (meaning, from now on, a 2-D representa-
tion of the globe) to represent areas truly and represent distances truly
and represent angles (i.e., shapes) truly. A good map will represent one
or more of these properties truly, but not all of them together. For example,
no map can be both conformal and equal-area. No map can be both equi-
distant and equal-area. Because of these di√erent types of distortion, car
ographers tell us that there is no single best map projection; the best
projection for one purpose may be poor for another. We will see examples
soon enough.
First, however, let us consider a map that is not projected. Why don't we
simply take the latitude and longitude coordinates of the globe, and map
them onto a plane? Say the x -axis is longitude and the y -axis is latitude.
Such an unprojected map of the world is shown in figure 4.4. 8 It distorts
scale and area everywhere except at the equator and distorts more at
greater distances from the equator. These distortions, however, are not as
area the surface is nearly flat. The sum of angles of triangles drawn on a sphere thus varies
with triangle size. Such is the weirdness of spherical geometry.
8. An unprojected map is also known as a plate carrée map, an equirectangular map, or an
equidistant cylindrical projection . The distances between parallels and between meridians is
the same everywhere on the map.