Map Projections - Spatial Mathematics: Theory and Practice through Mapping - page 191

longitude) are sent from the curved, two-dimensional, surface of a sphere to
a flat, two-dimensional, map is called “projection.” The transformation pre-
serves two dimensionality.
Imagine the Earth as an inflated balloon. Cut it open and flatten it. It will be
stretched in some places and shrunk in others. Distortion is inevitable. Since
the transformation from a bounded, curved two-dimensional surface to an
unbounded, flat two-dimensional surface is not a smooth one, every map pro-
jection is distorted in at least three, and sometimes in four, of the following
properties: Shape, area, distance, and direction. Thus, the challenge to the map-
per in choosing appropriate projections, as in selecting colors, data sets, and a
host of other variables, becomes, “but does it it or is it appropriate?” Readers
will have a chance to put theory into practice at the end of this chapter: Look for
example at links associated with the Mollweide projection in the theory section
and then practice selecting it, or other projections, in the later practice activities.
Readers with even deeper interests might wish to delve into the vast literature
on the topic of map projections and cartography, some of which is cited at the
end of this topic. Let us see why map projection selection might (or might not)
matter, beginning with a real-world story with some serious implications.
9.2 In the news. . .
In 2009, a fascinating blog appeared on the Esri website, apparently derivative
of an event associated with an Esri International User Conference (Maher, 2009:
http://blogs.esri.com/esri/arcgis/2009/07/15/the-buffer-wizard-in-arcmap/ ). Esri
ArcMap Team member, Tom Bole, had spotted a map that was published in
The Economist , May 1, 2003, which attempted to show the countries that could
be reached by North Korean missiles of different ranges. The map was made
simply by buffering Pyongyang, the capital of North Korea, without regard to
the underlying projection (a Mercator projection apparently had been used).
The result was to suggest that all of Europe, most of Africa, and most of North
America were not reachable by these missiles. Common sense might suggest that
clearly all of Alaska is within 10,000 kilometers of North Korea. Indeed, when
Bole checked distances, he found that the map portrayed a seriously erroneous
impression. He corrected the map, using a different underlying projection—one
on which buffer appearance and buffer distance aligned accurately, and sent the
correction to The Economist and it was published soon after, on May 15 of the
same year ( http://www.economist.com/node/1788311 ). The original choice of
map projection left most North American readers with the impression that they
were outside the range of North Korean missiles. When the underlying projec-
tion was corrected it became clear that any feeling of confidence about being out
of range was wrong. In local studies projection choice is often unimportant; in
global studies, however, a bad choice can produce devastating misinterpretation
(Maher, 2009). The phrase, “Don't believe everything you read” extends to maps,
as well! In order to avoid making bad choices, we also consider how projection