LIVE IN A PANHANDLE STATE?

There’s a formula for calculating it: (lots of geeky stuff and pictures at link)

pan handle
In this paper, we apply spatial analytical tool to address the question: Which geographic “panhandle” is more similar to a real panhandle?

Background: Panhandles

“Panhandle” is an informal geographic term for an elongated tail-like protrusion of a geographic entity that is surrounded on three sides by land regions not of the same administration. The term is derived, as an analogy, from the relation between the shapes and relative locations of a cooking pan and its panhandle. For example, the United States has panhandles such as the “Texas Panhandle” and the “Florida Panhandle.” Other countries, too have panhandles, such as the “Panhandle of Austria,” the “New Brunswick Panhandle” and the “Panhandle of North Korea.”

To the authors, the geographic term “panhandle” only captures some qualitatively geometry of the corresponding geographies, and there is no previous study addressing how close these panhandles are to a real-world panhandle. Because panhandle is defined in the context of a pan, answering the obvious question “Which geographic ‘panhandle’ is more similar to a real-world panhandle?” is equivalent to answering “Which U.S. state associated with a geographic panhandle looks more like a cooking pan?”

Data
To analyze the shape similarity between a cooking pan and portions of nine U.S states which are traditionally considered to contain a geographic “panhandle,” we collected boundary-shape information for those states (figure 1). Then we created an additional three polygons to mimic the shape of a cooking pan from the left side-view, from the right side-view and from the top-view (figures 2a, b and c). All polygon information was entered into GenToolTM, a cartography and geographic information system (GIS) software package, which we used to compute the shape similarities between the polygons that represent the cooking pan and the those representing the state boundaries.

Methods

We used Fourier descriptors to summarize the shape of boundary polygons. Suppose that one boundary polygon consists of N points, with the k-th point has coordinates pk (xk , yk), thus the boundary polygon can beparameterized as:

x(k) = xk , y(k)= yk

We then transformed this spatial information of polygon coordinates into information in frequency space, through discrete Fourier transformation. This allowed us to gain insights from a different perspective:

a(v) = F (x(k), y(k))

The Fourier descriptor acts much like moments in mathematics: lower order terms approximate polygons’ general shapes. Additional higher order terms refine the approximation by adding local changes. As an example, we reconstructed the boundary polygons by using the first 1st through 30th terms in the sequence a(v), and thus produce a series of approximations to the original polygons. These are illustrated in Table 1. We also performed the same Fourier transformation on the three polygons that represent the cooking pan.

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4 Responses to LIVE IN A PANHANDLE STATE?

  1. Leonard Jones says:

    This is like the taxpayer funded study about why lesbians are fat. One glance at the
    leftmost column and the question is answered. Someone spent way too much time
    brain-fucking this question!

  2. Steamboat McGoo says:

    Wonder why they left out Missouri?

  3. antzinpantz says:

    I guess they couldn’t handle it. 🙂

  4. Leonard Jones says:

    Bad pun Antz, but Steamboat did put it right over the plate!

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