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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

examples.

1

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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