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Maria Cicenas
Applied Mathematics
Weekly Summary 1
June 9 – June 16, 2009
Gerrymandering
This week my goal was simply to gather as much information as possible in order to evaluate the direction
in which I would like to further explore the topic of gerrymandering. I began by researching constitutional
requirements on congressional districts, current districts and current statistics on those districts. On the first
day of class, we discussed various parameters which could/do affect the creation of congressional districts;
therefore, I also located reliable sources for data on the possible parameters we discussed.
After looking at the congressional districts for the state of Kansas, and after the advice of fellow
classmates, I decided finding information on a more local level might not only be more interesting, but
would also give me to a better understanding of local factors that might need to come into play when
creating districts. Therefore, as done on the national level, I researched restrictions and located data for
creating districts on both the state and city level. As a side note, finding this information was much more
difficult than finding national information/statistics.
Finally, I researched mathematical approaches already attempted by others with regards to the
gerrymandering problem. I read the available research, and have listed those that I found credible and
possibly valuable in the attached Gerrymandering Resource File. (The file Kansas Maps includes maps
that I cited in the resource file, but saved as one document so I could access them quickly)
Unfortunately, after all that I have done, I feel that writing a program to create districts might be beyond my
limited coding experience (however, idea still slightly intrigues me). The new idea I would like to explore for
this upcoming week revolves around the idea of "compactness" (not in the mathematical sense ). From
what I have read the general public wants their districts "compact." If I can create a mathematical standard
for the "compactness" of a district, I can hopefully prove or disprove whether or not the mathematical
approaches already available indeed result in compact districts.
Maria Cicenas
Applied Mathematics
Weekly Summary 2
June 17 – June 23, 2009
Gerrymandering
This week I began my work by brainstorming for ideas on how I would like to define a compact
congressional district. I decided on expressing compactness as a ratio:
area of district
c
area of smallest circumscri bed rec tan gle
After testing a few examples, it seemed logical to further say that when 0.7  c  1a district is considered
compact and when 0  c  0.7 a district is not compact. For some states, odd coast lines and panhandles
make it near impossible for all their districts to fall into the compact category. At first I considered weighting
state borders differently than district borders, but then that isn't very fair to states like Kansas! Besides, the
main purpose of creating my definition was as a means to compare current districts to other possible, more
mathematical, districts.
My next task was to collect the data needed to begin calculating "c" for current congressional districts as
well as the districts created by the mathematician Dr. Warren D. Smith and Jan Kok (using the shortest line
algorithm) and Brian Olson (an algorithm based on finding the districts with the shortest distance to their
center). I found complete data on the area of the districts only for 13 of the 50 states. The data for the
other states was either incomplete or nonexistent. I used the data I did find and printed maps of the current
districts so that I could trace rectangles around them and calculate the compactness ratio. Although I did
have data for all 53 of California's districts, the small size of California's districts with respect to the large
size of the state made finding a good quality map and measuring the corresponding rectangles nearly
impossible. Therefore, I left California out of my data set.
I began finding the ratios for the shortest line algorithm as well. This process was much more time
consuming because I did not have the areas of the created districts. I estimated these areas by breaking
the districts into rectangles, trapezoids and triangles (Heron's Formula). Due to time constraints I did not
finish this process for the 12 states, and I have not yet begun the calculations on Mr. Olson's districts.
Because the borders of Mr. Olson's districts are mostly curves, and not mostly lines like the shortest line
districts, they should be even more difficult to calculate.
I am turning in a condensed version of the Excel spreadsheet I created (with only the data I collected and
not all 50 states) as well as a scanned example of the work I did by hand. I do have all of the work I did by
hand and will turn in a hard copy of that information, but I did not think it would be necessarily to scan all of
them (I doubt my classmates would need to see it); however, I will do so if you like.
For the upcoming week, I would like to examine the work of my Gerrymandering peers and see how I
could possibly contribute to their work. On the side, I will probably also work on finishing collecting the data
I started collecting this week so that I can have a complete set, or at least as close to complete as possible.
I will give a full analysis of my results then.