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The rectangularness of countries

pappubahry.com

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Re: The rectangularness of countries

#71
The site has run out of bandwidth allocation, so I'm only guessing what the metric is from the comments here...

I'd like to see it compared with a "parallelogramness" measure, based on rotating calipers. Rectangularity would be a special case.

https://en.wikipedia.org/wiki/Rotating_calipers

Re: The rectangularness of countries

#72
post #68

Earlier quoted context omitted.

Including Azores definitely affected the final result. It's weird that other countries didn't have their islands include though

Others are also affected by islands and territories, see France with French Guyana etc, Norway with Svalbard etc. France is quite a square country if you only consider its mainland so it is an odd choice to include non mainland areas but I guess it is a difficult greyzone on what to include and not.

The French themselves refer to metropolitan France as l'Hexagone so it probably still would not be a square.

Re: The rectangularness of countries

#73

this metric is kind of poor. What about something like the area ratio of the biggest inscribed rectangle to the smallest circumscribed rectangle that has edges parallel to the selected inscribed rectangle.

That measures nothing but outliers: consider that changing anything between the two rectangles would leave that metric unchanged.

It seems like it would be an excellent method if you could address the outlier issue though. One approach would be to relax the rectangles, so the outer one only has to circumscribe 95% of the country's area.

A similar approach is used in biology to define animal territories: A kernel density estimate is taken of historical animal positions and thresholded, rather than a minimum convex polygon.

Re: The rectangularness of countries

#74
post #13

Neat! To me, Egypt doesn't look very rectangular at all. The very deep concave section, and the sharp convex portion at the bottom right completely break rectangularity for me. I'm also curious as to why Nauru seems to have such sharp, straight borders - it looks more like the Vatican than a Pacific island.

The measure is how much overlap there is with a rectangle of the same area, which means that a narrow but deep deviation is weighted the same as a shallow but long deviation along the border. I'd think that an intuitive notion of "rectangulareness" (rectanglosity? rectangularity?) would better match some sort of RMS measurement, where the penalty for a mismatch is proportional to the square of its distance from the i…

RMS is a good idea. Maybe you would need an additional penalty for deviations near the corners, to prevent rounded countries from out-scoring those with wavy/angled but straight borders?

Re: The rectangularness of countries

#75
post #68

Earlier quoted context omitted.

Including Azores definitely affected the final result. It's weird that other countries didn't have their islands include though

Others are also affected by islands and territories, see France with French Guyana etc, Norway with Svalbard etc. France is quite a square country if you only consider its mainland so it is an odd choice to include non mainland areas but I guess it is a difficult greyzone on what to include and not.

Somehow I was thinking about France with French Guyana but must have passed it.

As some have said, I'd like to check the impact of only using mainland in the calculations.

Re: The rectangularness of countries

#76

Earlier quoted context omitted.

What do they say?

https://en.wikipedia.org/wiki/Winston%27s_Hiccup

Another good one is Bir Tawil, a piece of land that no country wants:

https://www.theguardian.com/world/2016/mar/03/welcome-to-the... https://www.youtube.com/watch?v=J5iJSXaVvao

Re: The rectangularness of countries

#77
post #18

I was kind of disappointed that this post isn't about artificial borders that look like straight latitudinal or longitudinal lines. Those kinds of borders are quite common and I've always thought they say a lot about a country and its past.

What do they say?

I came across this post on the Berlin Conference years ago and the title has stayed with me:

http://everything2.com/title/Never+Trust+a+Straight+Line+on+...

Re: The rectangularness of countries

#78
post #63

These are not rectangles though. The projection has severly stretched many of the countries. Combined with the tilted angles, that should mean the corners of these "rectangles" aren't really 90°.

Site is currently down, please tell me they used locally fitted projections, not Mercator?

Re: The rectangularness of countries

#79
post #13

Earlier quoted context omitted.

The measure is how much overlap there is with a rectangle of the same area, which means that a narrow but deep deviation is weighted the same as a shallow but long deviation along the border. I'd think that an intuitive notion of "rectangulareness" (rectanglosity? rectangularity?) would better match some sort of RMS measurement, where the penalty for a mismatch is proportional to the square of its distance from the i…

It's also good to realize that countries do not lie on a plane, and the edges of the rectangles should be great circle arcs.

Does this depend on the map projection used?
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