Lecture Materials, UP402
(as a supplement to, not
a replacement for, in-class material.)
Introductions; project interests.
Website and syllabus
Biosketches: include background project interests.
Latitude and Longitude
to brief explanatory material
Lab--set up website, discuss project interests.
Coloring of maps;
Choropleth maps; Color; Grayscale; Four Color Theorem (choosing
numbers of colors)
Given that no more than four colors are ever needed to color a map in
the plane, why should a GIS have so many choices for color?
Choropleth maps with many ranges need a variety of colors
Ranges need to make sense so that changes in data intensity are reflected
in changes in color intensity
Grayscale and color, this parallelism about data and color intensity
Four colors are sufficient to color any map in the plane; one never
needs more than four. Thus, when choosing coloring schemes, bear
this fact in mind and have a rationale for color selection based on the
underlying known theorem about coloring. One such good rationale
is offered above, involving choropleth maps.
Open research questions: coloring issues with different forms
of polygon adjacency; coloring on different surfaces (some solved earlier--extra
5. Page 6.Page
color map). We may return to these later when we discuss map
transformations of various sorts.
Lab: websites and projects
Matt Naud, guest lecturer, for two hours.
Lab--visit to City of Ann Arbor Planning Commission (or substitute),
time to be announced, later.
Field evidence. Use of GIS in an integrated report.
projection: Stereographic projection.
The One-point Compactification Theorem (blackboard
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. Thus, there can be no perfect map in the plane.
Four Colors are sufficient for any map on a sphere,
as well. An application of the one-point compactification theorem.
Map projection as a transformation: Thompson's
to various projections.
Handouts on Map Projections
Classification--move the center of projection;
alter the plane of capture (roll it up into a cylinder, torus, Möbius
strip, or Klein bottle--developable surface; try a cone).
Cylindrical and conical projections--choose a
projection suited to need.
Mercator--conformal--well-suited as a navigation
chart. Equal area projection better-suited to showing map of the
1. Paul Perrault
2. Dan Burt
3. Tina Meltzer
4. Chris Eckman
5. Alzena Saleem
6. Sarah Velarde
7. Kara Huizdos, Jennifer Gillis
8. Brad Fuzak, Alan Striegle, Adam
Pettinger, Kathryn King
9. Ron Keolian, Rachel Hornstein,
Syria MIS, see pop-up menu on main page
Bromley NIS, see pop-up menu on main page
Centrality and Hierarchy -- from the classical
to the modern. Using the classical for alignment to extend into the
modern setting--a strategy useful in a wide range of theoretical and applied
Material on a geometric model of Central Place Theory (Christaller/Lösch).
Classical central place theory--basic
K=3 hierarchy, marketing principle
K=4 hierarchy, transportation principle
K=7 hierarchy, administrative principle
Fractal central place theory.
Illustration of exact fit of the two approaches, showing that the fractally-generated
tiles fit together precisely to form the classical central place landscapes.
Week 13. No class, Thanksgiving recess begins at 5:00p.m.
Summary--look over website and think about where we have been (also
in connection with "five themes": Location; Place; Human/Environment
Interaction; Movement; Regions).
Older equipment--how maps were once made (not all that long ago!)--hands-on
with older equipment--Rapidographs, Leroy Lettering Set, Zip-A-Tone (dry
transfer lettering and screening),...