Scale - Spatial Mathematics: Theory and Practice through Mapping - page 110

Geological Survey (USGS), at these three scales. Maps in the 1:24,000 series
depict an area that is 7.5 minutes of latitude by 7.5 minutes of longitude. In the
1:100,000 series, standard map size is 30 minutes of latitude by 60 minutes of
longitude. In the 1:250,000 series, the standard map size is one degree of lati-
tude by two degrees of longitude. The grid shown in Figures 5.1a-c depict
the amount of area covered by maps at each of the three scales. The amount
of territory depicted on each of the maps indicated by each “grid cell” is
different because the scales are different. The shape of each of the map “grid
cells” appears rectangular but it is actually an isosceles trapezoid because as
you recall from our earlier discussion in this topic, meridians converge at the
poles. Scale, and geometry, matter!
5.2 Scale change
The Representative Fraction is of particular importance in showing changes
in scale ( Figure 5.1 ) . Because the fraction 1/24,000 is larger than the fraction
1/50,000 (cut two equally sized pies into pieces—the pieces are smaller when
50,000 are cut than when 24,000 are cut), the map of scale 1:24,000 is said
to have larger scale than the map of 1:50,000. Often, maps are called “large
scale” maps. But, to give meaning to that phrase, there must be another map
to which it is being compared. Certainly, the 1:24,000-scale map is the largest
scale map in the set of three maps in Figure 5.1 . Clearly, the 1:250,000 map
is the smallest scale map in this set because the fraction 1/250,000 is smaller
than either of the other two fractions. Is the map with a scale of 1:50,000 a
large or a small scale map? The answer is that it depends on the context. In
relation to the 1:24,000-scale map, it is smaller scale. But, in relation to the
1:250,000-scale map, it is larger scale.
Typically, topographic maps produced at 1:24,000 show natural features
including rivers, valleys, and vegetation as well as constructed features such
as railroads, roads, and buildings. The contour lines show the elevation above
mean sea level. Maps at this scale are often used for urban planning proj-
ects, environmental management, and a variety of outdoor activities. Both the
1:100,000 series and the 1:250,000 series, no longer updated by USGS, show
features similar to those shown in the 1:24,000 series but not in as much
detail. Try your hand at creating maps at a variety of scales, online, using the
MapMaker tool in the National Atlas. Zoom in to enlarge the scale and zoom
out to reduce the scale. As we saw above, the terms “large” and “small” scale
are relative terms and have meaning only when there are at least two maps
considered in the discussion. That is because the reference is to comparison
of representative fractions. Often, however, folks simply look at a map and
say that because it shows detail it is a large scale map, or that because it
shows a broad area without a lot of detail that it is a small scale map that is
“generalized.” In reality, however, all maps are generalized representations of
the Earth, even those that show great detail. A map is only a representation