Map Projections - Spatial Mathematics: Theory and Practice through Mapping - page 197

intersection points. The greater the associated distortion in mapping the globe
to the plane, the greater the distortion of the circle, which will be shown
either as an enlarged circle or as an ellipse with long major axis in relation to
its minor axis.
The Mercator projection is based on the geometrical idea of a cylindrical
projection. Figure 9.3 shows how a Mercator projection distorts the rela-
tive sizes of land areas on the Earth: As one moves toward the poles, areas
are increasingly enlarged. The Tissot circles correspondingly enlarge with
movement toward the poles. They do indeed reflect the underlying landmass
enlargement associated with the manner of projecting the surface of a sphere
to the plane. Choose a Mercator projection as a navigation chart at sea—it
shows true compass bearings. Do not choose a Mercator projection to make
land area comparison—Greenland will be larger than all of South America!
Figures 9.4 and 9.5 reveal elongation (enlargement and shape distortion)
of Tissot ellipses on two different pseudocylindrical projections: Mollweide
and sinusoidal, respectively. What differences do you detect in the pattern of
meridians in these last two figures? Note that in the case of the Mollweide,
the meridians are halves of ellipses while in the sinusoidal, they are halves
of one period of a sine wave. What are their implications for mapping? Note
that one of them shows greater compression at the poles than the other. At
Figure 9.3 Tissot's Indicatrix, Mercator projection. Source of original image: Eric
Gaba, June 2008. Data: US NGDC World Coast Line (public domain). Extra mate-
rial (Weisstein, 1999: http://mathworld.wolfram.com/MercatorProjection.html ).