Conceptual Material summarized from last
The Jordan Curve Theorem:
permits correct assignment of addresses on either
sides of streets
permits visually appropriate coloring of polygons
illustrates the need to split complex curves apart
at nodes where the curve crosses itself in order to ensure that the two
properties above will hold on maps. This fact is important in digitizing
The Four Color Theorem:
shows that four colors are enough to color any map
in the plane with adjacency of regions defined across an edge only.
suggests that if distinctions need to be made that
correspond to gradations in data, that a graded scale of four, and often
more, colors will make appropriate distinctions among regions
The One-point Compactification Theorem:
shows that the skin of a spherical globe cannot be
perfectly flattened into the plane; it fails to do so by at least one point.
that there (therefore) can be no perfect map in the
Small Group Discussions
Useful extension: go to www.usgs.gov and search the site for "spatial
tools" and for "animal movement." These tools are free and are run
along with Spatial Analyst Extension to ArcView.