States Based on Closest State Capital

On November 2, 2014 · 8 Comments

Twelve Mile Circle receives a fair amount of reader mail and suggestions. Usually it leads to pleasant surprises and sometimes even an article. That was the case recently with a map generated by Steve Spivey who graciously granted permission for me to share it with the 12MC audience.

Steve had been combing through the very earliest days of the site and came across Remote Southwestern Virginia, an article first published in November 2007. It demonstrated that Lee County in Virginia, the southwesternmost corner of the state, was closer to eight state capital cities (and possibly nine depending on measurement) than it was to its own state capital of Richmond. This also fascinated me at the time and spawned the Worst State Capital Location along with various other capital-related articles.

However Steve took a completely different angle by creating a Voronoi diagram(¹) with each state capitol building serving as a generating point. What if states were reshuffled based upon the closest existing state capital? Forget about geographical barriers, history, culture, politics and maybe hundreds of other practical considerations by reducing the problem to a purely mathematical process. As an example, the 12MC headquarters is based in Arlington, Virginia. It’s 106 miles (170 km) from Richmond and only 39 miles (63 km) from Maryland’s capital in Annapolis. Mathematically a reconstituted Maryland might be a better state for me if distance was the only consideration and nothing else mattered.

Let’s take a look at the resulting Voronoi diagram, and of course feel free to open the image in another tab to experience the effect in full-sized glory.


States Based on Closest State Capital

Some states would become winners, other losers and some like Maine and Washington would remain largely unchanged. Alaska and Hawaii would be unaffected because of their remoteness so they were excluded. Chicago would become part of Wisconsin, New York City would be absorbed into New Jersey, and the Los Angeles metropolitan area would split between California and Arizona. Parts of Texas would be cleaved into four neighboring states.

The smallest states, Rhode Island and Delaware, would become major beneficiaries. They would retain their existing geographic integrity while picking-up surrounding territory. Rhode Island and Connecticut would encroach on Massachusetts to such an extreme that Massachusetts would transform into the new Rhode Island (i.e., the new smallest state). Virginia would get squeezed considerably although why would I care? I’d live in Maryland. Meanwhile, neighboring West Virginia would grow to become the unquestionable king of Appalachia.

Many of the states farther west would continue as territorial behemoths although their familiar shapes might soften or erode entirely. North Dakota would maintain it familiar rectangle although larger. Idaho, on the other hand, would transform into an unrecognizable diamond.

Anyway it was a fun diversion although otherwise kind-of meaningless. That made it a perfect balance of intellectual silliness that sent me along a mental tangent for awhile. I loved examining the map, each time finding something different as I imagined the new world order.


States Based on Closest State Capital with DC

Steve took the game one step farther. What if we considered the District of Columbia as a state-equivalent and included it within the calculation? That of course would require us to set aside even more practical considerations including an obvious Constitutional question(²) although none of those mattered for this exercise. It would impact only the Mid-Atlantic region as pictured above. My residence would become part of the new, larger Washington, DC, while Maryland would reduce to a narrow strip hugging the rim of the northern Chesapeake Bay anchored by Baltimore.

Steve was thinking about producing similar maps for Canadian provinces as well as a worldwide version. We should encourage him in those pursuits. Thanks Steve!

(¹) A Voronoi Diagram is "The partitioning of a plane with n points into convex polygons such that each polygon contains exactly one generating point and every point in a given polygon is closer to its generating point than to any other. A Voronoi diagram is sometimes also known as a Dirichlet tessellation. The cells are called Dirichlet regions, Thiessen polytopes, or Voronoi polygons."
(²) Article I Section 8 of the U.S. Constitution specifies that the District shall "not exceed ten Miles square. So we’d need to amend the Constitution. No problem.

On November 2, 2014 · 8 Comments

8 Responses to “States Based on Closest State Capital”

  1. Craig says:

    While this is a fascinating exercise, in practical terms of course, what people care about would be the much harder travel distance (i.e. time driving, flying, training, etc.) rather than absolute distance minima. I know that that’s too computationally difficult, but it’s worth thinking about.

    I wonder if one could conversely set up a problem where one moves state capitals around to optimize their positions within their current state borders, vis-à-vis the other state capitals – sort of the opposite of Steve’s problem. One would attempt to move the capitals to create polygons that caused the least change in current state boundaries.

    • Steve Spivey says:

      I think a quick answer would be to move the capitals to the geographic center of each state, but I’m not certain how the outlines would look. Maybe I will work on that another day.

  2. January First-of-May says:

    I wonder whether the distances are true great-circle ones or just the ones on a map (and, equivalently, whether the dividing lines are actual great circles or just straight lines).

    Alaska and Hawaii are only unaffected because of where the capitals are located (in the parts of the respective states that are closest to the lower 48). Of course, if we add the five territories too, things become funny.

    • Steve Spivey says:

      They are not perfect great circles, but very close. The original map was adjusted to minimize the curvature of Earth, which wasn’t too excessive to start.

      I did run a few of the outer “tri-state” midpoint coordinates, manually plugging them into Google Earth, and they were approximately where my map shows, maybe off 1-3 pixels at most.

      I do want to make a Google Earth kml, but I have to figure out how to get a program to calculate ~50 midpoints, instead of the 100K+ (48*47*46) possible. That would be 1 crowded map.

      I had not thought about the other 5 territories, I think they would all be far enough away from each other that it wouldn’t change anything.

  3. h says:

    Pittsburgh is interestingly affected by this — it is split right in the middle of its county, Allegheny, between three states!

  4. Rhodent says:

    Is it my imagination, or is the map showing a tiny portion of Pennsylvania (near Erie) that forms a non-contiguous portion of Michigan?

    • January First-of-May says:

      I’m seeing it too, particularly on the second map (and it might even include some of nearby Ohio).
      Alas, from what I could see on the radius tool, Erie Bluffs (a place well within where that portion would be) is a lot closer to Columbus OH than to Lansing MI; the actual OH/MI/PA midpoint would be well within Lake Erie this way. Not sure if it’s due to the map imperfection or just a misplaced Columbus, however.

      On the second map, it might not be obvious that there is, in fact, a Maryland-Virginia land border (near the lower end of that “peninsula” in southern Maryland – which is actually a chain of islands, but the boundary appears to cross one). The above-mentioned radius tool places it on Goose Island specifically (and yes, I had to manually check a few candidate locations to find that).

    • Steve Spivey says:

      That is just an aberration of the map’s curvature. The actual tripoint should be closer to Toronto than to the PA shores.

      If only we can get a Kickstarter fund to turn the Earth into a cube, mapping would be so much easier. 🙂

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