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A spatial science
The mathematical power of gIS clearly
emerges in its capacity for spatial analy-
sis, whereby the software probes the data
in terms of its geographic, geometric,
and topological properties. This primary
tool includes various set theory func-
tions. In Figure 3, I have created a shared
habitat range map for African elephants
and giraffes. I used a robinson projec-
tion, which was for many years the most
popular representation found in textbooks.
Math teachers will recognize this map as
an intersection of two sets. Other functions
Figure 3 available are union, subtraction, distance,
crossing, and containment—all processes
that are simple with small number sets
but extremely arduous with the masses of
geographic data that studying even a small
region can generate.
Large collections of data pose tangible
problems for students. gIS manages that
data immediately. In Figure 4, I have cut
from a data layer about world cities to fit
the South American continent in a Merca-
tor projection. That new layer has been
disaggregated into a histogram, with thirty
“bins” (categories based on population).
The student mapmaker now has a wide
range of statistical information telling him
or her that South America’s city population
Figure 4
data is skewed by three megacities: Bue-
terms, paper maps are a two-dimensional nos Aires, rio de Janeiro, and Sao Paulo.
representation of a three-dimensional, gIS reveals its true identity as a spatial
curved surface. even in the open ocean, science.
the horizon is a mere three miles away
when standing on the deck of a boat one
meter above the water. gIS adjusts for
Learning from data
the curvature of the earth, as in these
In Figure 1 (a Miller Cylin- In discussions about population and race,
drical projection), the distance between it became clear that students had a mis-
Los Angeles and New york City is 2,465 conception that urban areas and Southern
miles. The path is curved to demonstrate states had a higher percentage of African-
the shape of the earth. In Figure 2 (an American residents. We investigated this
Orthographic projection), the distance question while learning about scatter plots.
is the same, but the path is now straight A scatter plot provides a graphical display
because the projection is spherical. The of the relationship between two variables.
software can measure in kilometers, The vast array of data available from the
meters, miles, yards, feet, or nautical U.S. census is a fertile field for teaching
miles. Try that with a ruler. the concepts of correlation and distribu-
tion. A correlation between the variables
results in the clustering of data points
along a “best fit” line. In Figure 5, a scat-
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