Mapmaking - The Science of Navigation - page 96

incorrect, or both. Di√erent types of projection can preserve one or other
of these navigational figures—distance or angle—but not both.
There is another property that we need to consider: the area of a country
or continent. A true representation of the globe will preserve the areas of
di√erent regions of the globe. Thus, there are three types of distortion that
can arise when a globe is projected onto a 2-D map:
≤ Area . A true map will be equal-area , meaning that the relation-
ship between areas on the map is the same as the relationship on
the globe. In other words, the map scale is true everywhere. For
example, South America has an area of 17,840,000 km 2 (a little
under 6.9 million square miles), whereas Greenland's area is
2,166,086 km 2 (say 835,870 square miles), so South America is
about 8 1 ⁄ 4 times bigger. A 2-D map that is equal-area will preserve
this ratio as well as the ratio of any other two areas on the globe. 6
≤ Distance . No 2-D map can preserve all the distances between two
points on the surface of a globe. This will become clear when we
look in more detail at map projections. An equidistant map is one in
which distances in certain chosen directions are correctly repre-
sented. For example, an equidistant map centered on New York will
show the true distance from New York to London, and from New
York to São Paulo—but not from London to São Paulo.
≤ Angle . A conformal map preserves the angles between points on the
globe and therefore preserves the shapes of areas. In fact, this usu-
ally works only locally, meaning over a small area. Thus, if we draw
a line from Baltimore to Washington, DC, to Philadelphia, the angle
at Washington on a conformal map equals the angle measured on
the globe. 7
6. Does your map of the world show Greenland to be larger than the Democratic
Republic of the Congo (Zaire)? If so, your map is distorting areas; the DRC is 8% larger.
7. The angles of a triangle add up to 180\, as you may recall from high school. However,
this is true only on a flat plane, such as a piece of graph paper. On a globe, the three angles of
a triangle add up to more than 180\. For example, consider a triangle drawn from latitude 0\
and longitude 0\ (on the equator just o√ the coast of central Africa) to latitude 90\ north
(the North Pole) to latitude 0\ longitude 90\ west (just north of the Galapagos Islands).
Each of the angles of this triangle is 90\, so the sum is 270\. (The spheres of fig. 4.5 are
divided into eight such triangles.) Smaller triangles on the globe (with each leg of the
triangle much smaller than the earth's radius) have angles that add up to a smaller number,
much closer to 180\ though still bigger. This is why conformal maps preserve angles only
locally—over a small area surrounding a given point on the surface—because over such an