Geometry of the Sphere - Spatial Mathematics: Theory and Practice through Mapping - page 26

1.6.4 Latitude and longitude, hemispheres, and precision
Start a web browser session and access ArcGIS Explorer Online ( http://explorer.
arcgis.com ). Start a new map. Change the base map to National Geographic. In
the search box, enter 39.58841, 105.64335 for the latitude and longitude, respec-
tively. As indicated earlier, some GIS tools such as ArcGIS Online force coor-
dinate entry as latitude, longitude ( y , x ) rather than longitude, latitude ( x , y ).
Zoom out until you can recognize some landforms and countries. What country
are you in? Recall the discussion in this chapter about latitude and longitude
and the Cartesian coordinate system. You are in the northern and eastern hemi-
spheres because both the latitude and longitude values are positive. As you
zoom out to a smaller scale, you will see that you are in China. In the search
box, now enter - 39.58841, 105.64335, making sure this time that the latitude is
negative. In what hemispheres is this location, and why? In what ocean is this
location? What is the nearest continent? Use the measurement tools to measure
the distance to it, indicating the units you are using and the cardinal direction
in which it lies in relation to the point. You are now in the southern and eastern
hemispheres, because your latitude is negative and your longitude is positive,
in the Indian Ocean, about 630 miles southwest of Australia.
Next, in the search box, enter - 39.58841, - 105.64335, making sure this time
that both the latitude and the longitude are negative. In what hemispheres
is this location, and why? As you did with the previous location, indicate the
nearest continent, the distance to it, and its cardinal direction. Change the
base map to topographic. Now you are in the southern and western hemi-
spheres, because your latitude and longitude are both negative, putting you
in the lower left of the Cartesian coordinate system as cast on the world.
Specifically, you are in the Pacific Ocean, about 1,700 miles due west of Chile.
Next, in the search box, enter 39.58841, - 105.64335, making sure this time
that the latitude is positive and the longitude is negative. This time, add your
point to map notes (using the plus sign on the location pop-up to pull up a
menu with “add point” as an option), and a push pin should remain in this
location. What mountain is the map centered on, and what is its elevation?
Zoom out until you see the state and country. What state and country is this
mountain in? In what hemispheres is this location, and why? This is Mount
Evans, Colorado, USA, and is located in the northern and western hemispheres
because its latitude is positive and its longitude is negative.
Now let us visualize how precision manifests itself on maps and why it mat-
ters. Zoom back to 39.58841, - 105.64335. Use the search box to search for
39.5884, - 105.6433, thus removing one significant digit off of each of the lati-
tude and longitude values. Add your point to the map notes. How far is this
point from the summit of the mountain? In what direction is this point from
the summit of the mountain, and why? Remove one more digit and search
for 39.588, - 105.643, again adding it to the map notes. How far is this point
from the summit of the mountain? In what direction is this point from the
summit of the mountain, and why? Remove one more digit and search for