
The rectangularness of countries - outputchannel
http://pappubahry.com/misc/rectangles/
======
filvdg
For people who like complex borders

[https://www.google.be/maps/place/Baarle-
Hertog/](https://www.google.be/maps/place/Baarle-Hertog/)

This is a Belgian city enclave within the Netherlands with enclaves of the
Netherlands within its borders

~~~
djsumdog
Wow. I feel like there should be a CGP Grey video about this. He has one about
London vs the City of London and the weird US/Canada border.

Someone also tried to tell me Norwood, Ohio is the largest city within a city
(an enclave city), but I can't find a source on that anywhere.

~~~
acheron
What's weird about US/Canada? I thought it was pretty straightforward. Was
this about the "Angle" on Lake of the Woods?

~~~
stephengoodwin
There's the exclave Point Roberts, Washington
([http://ngm.nationalgeographic.com/ngm/0408/feature7/](http://ngm.nationalgeographic.com/ngm/0408/feature7/)),
which falls ever so slightly south of the 49th parallel.

~~~
lisper
I once visited Port Roberts just to see the border crossing. I drove in from
the Canadian side, parked my car, and walked across the border into the U.S.
without being challenged. No one asked for my passport. As far as I could
tell, no one even noticed that I had crossed the border. But when I tried to
walk back into Canada the Canadians gave me a pretty hard time and almost
didn't let me back in. It was an interesting experience.

~~~
haberman
I've visited there too. Drove in both directions, seemed like not a big deal.

I heard that kids there go to school in Blaine, which means 4 international
border crossings every day!

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bbctol
It's a good metric, but I do feel there's something slightly different being
said in human terms when we say a country is "rectangular." Turkey seems to
have sharper, closer to 90 degree angles than other countries that may overlap
a rectangle more.

I suspect what's really going on, psychologically, is that Turkey looks much
more like a rectangle than it does any other basic shape: I would never
described Macedonia as rectangular, despite its considerable overlap, because
it's "oval." Kenya's a pentagon before it's anything else, and so on.

~~~
zem
right. Côte d'Ivoire in particular has a very high score while "looking"
nothing like a rectangle

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Analemma_
I'm surprised Portugal didn't score higher. One day in the car I randomly
asked myself the same question of "which country is the most rectangular", and
Portugal was the first one I thought of. Is it because the Azores were
included? Would like to see the rank if they had only the mainland.

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

~~~
flurdy
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.

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

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jwilk
509 Bandwidth Limit Exceeded

Here's an archived copy: [https://archive.is/cRkgb](https://archive.is/cRkgb)

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etatoby
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.

~~~
JumpCrisscross
What do they say?

~~~
vec
Long, straight lines for borders usually imply that the territory through
which they are drawn was neither well explored nor terribly important to the
people drawing them. Sometimes that's because the territory is mostly
uninhabited and nobody really has a strong claim to want their particular
patch of land to be on one side or the other, but frequently its because the
mapmakers either don't know or don't care about the cultural affinities and
loyalties of the people who live on or near the proposed border.

This is one of the main reasons why a lot of central Africa is a shit show
politically. Most of the modern borders were drawn during the colonial era
without much consideration as to which tribes and city-states ended up in
which countries, so there's not a strong relationship between "nations" (i.e.
culturally similar groups of people) and "countries" (i.e. demarcated
stretches of land) like there is in most of the rest of the world.

~~~
asimjalis
How does this reasoning apply to the US-Canada border?

~~~
niftich
It applies perfectly. The 49° N section of the border was set in the Treaty of
1818 [1], at which point all affected regions were still populated by native
americans.

You can see on this territorial expansion map [2] of the United States, how
the lay of the border differs between the first-settled east and the later-
settled west.

[1]
[https://en.wikipedia.org/wiki/Treaty_of_1818](https://en.wikipedia.org/wiki/Treaty_of_1818)

[2]
[https://upload.wikimedia.org/wikipedia/commons/2/29/UnitedSt...](https://upload.wikimedia.org/wikipedia/commons/2/29/UnitedStatesExpansion.png)

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theoh
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](https://en.wikipedia.org/wiki/Rotating_calipers)

------
pavel_lishin
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.

~~~
mikeash
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 ideal rectangle. It would be really
interesting to see what changes with that sort of measurement.

Regarding Nauru, I think that's just poor resolution in the source data. It's
only a couple of miles across, and the plot looks like it attempted to
approximate the coastline with points roughly 1 mile (maybe 2km?) apart.

~~~
akavi
There's a couple of different scoring rules that would be interesting, I
think.

Another one might be: What's the ratio between the area of the country and the
smallest rectangle which bounds the country. This would "punish" countries
with protuberances more than ones with "in-cuts", which "feels right" to me.

~~~
mikeash
For some reason, your use of "'punish' countries" made me imagine a world
where improving this score gets taken seriously by the peoples of the world,
leading to countries gradually becoming more rectangular over time, and many
terrible wars along the way.

~~~
clock_tower
This reminds me of Paradox's strategy games, where players routinely complain
about "bordergore" and fight wars to make the map look neater...

~~~
mikeash
That's great, never heard of that before. When I search for that term, the
first hit is a Reddit thread where the first commenter expresses his desire to
"drop-kick" people who do it. Strong emotions! Maybe we can create this world
after all.

I wonder how many actual wars in the past have been started because someone
didn't like how the border looked on a map. It has to be non-zero.

~~~
jlg23
> I wonder how many actual wars in the past have been started because someone
> didn't like how the border looked on a map.

Plenty, though it's less about rectangular shapes per se but borders being
drawn by former colonial forces with a ruler, splitting ethnic groups and
forcing them to live under a new, foreign government. Under colonial rule
every unrest was simply stopped by brute force, after "liberation" and
division of countries according to some arbitrary border created by drawing a
line along a ruler on the map there was no "moderating" force anymore and
ethnicities that had ignored/evaded each other for centuries were forcibly
mixed and the former colonial force usually decided who was the new
government, based on their interest. A great example is Western Sahara:

Spain left and decided "this part goes to Mauritania, this part goes to
Morocco". The Sahawri managed to beat the Mauritanian forces and to claim some
land, then Morocco "invaded" (in quotes because Moroccans fought the Spanish
in the 50s from as far south as Aoussard). Also, officially the border between
Morocco and Algeria is closed because of Algerian support for the Sahawri. But
in the north of Morocco, in the Rif area, people feel more connected to the
Rif than to Morocco and cultural exchange with the Algerian Rif people is much
more vibrant than cultural exchange with the south of Morocco.

------
jpindar
I wonder how many of those are due to pairs or rivers or mountain ranges that
tend to lie parallel to each other, or to rivers that tend to be at right
angles to a coastline?

------
dnautics
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.

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

~~~
bckygldstn
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.

------
tobr
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°.

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

~~~
rspeer
They used an equirectangular projection, because rectangles. But that means
that some of these rotated rectangles are more like parallelograms when you
look at them in another way.

Mercator actually would have been a good choice because it preserves local
angles. Not sure why you'd be so opposed to it in this case. For this purpose,
relative sizes don't matter at all.

And I don't think a local projection would clarify anything. Countries can get
pretty big and non-local. If you strive for complete geometric accuracy on the
scale of, say, Canada, the idea of a "rectangle" breaks down because there are
no parallel lines on Earth, and four right angles don't bring you back to the
orientation where you started.

------
hyperpallium
I have a theory that newer borders more rectangular, whereas older borders
follow natural wiggly features like rivers, similar to newer cities' roads
being more rectangular, whereas older roads are more higgly-piggly organic.

The older ones grew; the newer were planned.

You can see it east-to-west in the USA states' borders.

------
andrepd
I'm not sure this algorithm is the best fit for our natural intuition of a
rectangular country.

------
shekhar101
I read somewhere that manmade boundaries can be clearly identified. They are
mostly straight lines on maps. It makes more sense after reading this article.
This is the reason why so many African countries have such sharp boundaries.
Colony masters divided them amongst themselves, ignoring natural resource
division, people and ethnicity of new countries. This has led to so many
conflicts among these countries as well. I might be wrong, but I think this
happened to middle-east as well.

------
ProfChronos
Funny to see that France is only 134th while French refer to their country as
"The Exagon" (metropolitan France) - 3 ground borders and 3 sea borders. The
expression was coined in the 1860s by school reformists and got popular after
the Franco-German War in 1870 when Alsace was lost. To my knowledge French are
the only ones to define their country with a geometrical form

~~~
lagadu
Portuguese people also generally see our country as a rectangle too. And no,
the islands don't count.

------
Isamu
You mean xkcd hasn't covered this already?

------
TheRealPomax
Wow, what's going on with the Netherlands

~~~
mrweasel
The Netherlands have two islands in the Caribbean that is technically no
different than any other "county" of the Netherlands.

~~~
clort
which are these? as far as I understood (I lived in Sint Maarten for a couple
of years once) the Netherlands Antilles are colonies only, unlike the French
islands (Martinique and Guadeloupe mainly, but St Barts and St Martin too)
which are overseas departments of France, and also considered part of EU.

~~~
Someone
The kingdom of the Netherlands consists of 4 countries: Aruba, Curaçao, St
Maarten, and the Netherlands.

In name, they are each other's equal within the kingdom, but there is a
'slight' difference in size.

Also, 3 other islands in the Caribean are part of the Netherlands, the
country: Bonaire, St Eustatius and Saba (but, if I have to believe Wikipedia,
those 3 are not in the euro zone; the US dollar is legal tender in (part of)
the country of the Netherlands)

([https://en.m.wikipedia.org/wiki/Kingdom_of_the_Netherlands](https://en.m.wikipedia.org/wiki/Kingdom_of_the_Netherlands))

The French have more overseas areas, and manage to make things complicated,
too, with overseas departments, countries, territories, and collectives
([https://en.wikipedia.org/wiki/Overseas_departments_and_terri...](https://en.wikipedia.org/wiki/Overseas_departments_and_territories_of_France))

------
ihaveajob
The site is out of bandwidth, so this might help:
[http://webcache.googleusercontent.com/search?q=cache:http://...](http://webcache.googleusercontent.com/search?q=cache:http://pappubahry.com/misc/rectangles/)

------
dredger
Something doesn't seem right about this algorithm you used to draw the
rectangles. If you used a similar algorithm to define circles, I feel like you
would get a artificially high amount of circularness for countries that are
not that circular.

~~~
elcapitan
Or probably just any kind of polygon from triangle to whatever you choose to
find. The common property is probably rather convex shape than rectangularness
or anything arbitrary like that. Maybe because convex borders are easier to
protect or less threatening to neighbors or something like that?

------
temuze
Would be nice to apply this to gerrymandered congressional districts.

------
schneidmaster
Huh, the US is 169 out of 208. I would've guessed it at a good bit higher but
I forgot Hawaii and (especially) Alaska are kinda hanging out there screwing
up the ideal rectangle.

~~~
foota
The metric used doesn't really knock us for Hawaii though, because it's so
small.

------
fiatjaf
Correlate with economic development!

~~~
notsureifwant
There's a fair amount of research in economic history on almost exactly this
topic. Two recent papers
[http://www.nber.org/papers/w12328.pdf](http://www.nber.org/papers/w12328.pdf)
and [https://drive.google.com/file/d/0B4s_WKe-
US99LV9XVTNVNzFxYW8...](https://drive.google.com/file/d/0B4s_WKe-
US99LV9XVTNVNzFxYW8/view?usp=sharing) have looked at how measures of the
artificial-ness of borders (how straight they are, how often they cut through
the territory of ethnic groups, ratio of a country's area to the area of its
convex hull) are correlated with various measures of welfare (e.g. GDP/capita,
lack of conflict). The papers are often controversial because they often claim
something approaching causality (see recent Twitter war
[https://twitter.com/bill_easterly/status/753252113510268928](https://twitter.com/bill_easterly/status/753252113510268928)).

~~~
fiatjaf
Who are these people discussing on Twitter? Are they the researchers who
publish papers on the topic? (I do not mean these same papers you linked to,
just asking if they are serious academics.)

~~~
notsureifwant
Easterly is an economist at NYU (who published one of the earliest papers on
the subject), I'm not sure about the others. However the discussion is a good
representation of some of the debate that's gone on regarding interpreting
correlations between regular-ness of borders and GDP (i.e. is it that having
artificial borders was disruptive, or was it that borders were drawn
artificially in areas that had fundamental characteristics which have caused
them to have lower GDP today).

------
zumu
I wonder if the overall rectangularness of the African countries is evidence
of a bias for retangualarness by the map making colonial powers.

~~~
LeifCarrotson
Egypt and Equatorial Guinea are clearly on latitude/longitude lines, but the
rest look pretty random. I am actually surprised that it's as nonlinear as it
is - go take a look at a map of Africa, not much is actually rectangular!
There are a lot of straight lines (which would be another interesting metric
to study-the countries most closely bounded by an irregular polygon) in
several interior borders on the Sahara, as well as Namibia and its neighbors.
But none except Equatorial Guinea are really rectangular.

The state borders, on the other hand, are often quadrilaterals. Perfect scores
to Wyoming and Colorado, and near-perfect for many others.

------
SteveCoast
Colorado wins

~~~
a-priori
Another example is Saskatchewan, Canada. Like Colorado, its borders, on all
four sides, are defined by latitudes and longitudes.

~~~
niftich
Saskatchewan actually has an unusual border on its east with Manitoba, in
which a series of north-running meridians are interrupted by west-running
jogs. This newspaper piece [1] reflects on the story behind this boundary.

[1] [http://www.theglobeandmail.com/opinion/why-the-zigzag-
betwee...](http://www.theglobeandmail.com/opinion/why-the-zigzag-between-sask-
and-man/article4202831/)

------
known
[https://en.m.wikipedia.org/wiki/List_of_active_separatist_mo...](https://en.m.wikipedia.org/wiki/List_of_active_separatist_movements_in_Asia#India)

------
gavinpc
169/208?

Reagan would never have let this happen. #makeamericarectangularagain

------
thomasahle
I wonder how similar the result would have been with this metric:

Score = area of the symmetric difference between country and the rectangle
maximizing the score.

------
D_Alex
Eq. Guinea at #18 looks wrong...the rectangle seems too large. It is pretty
rectangular, about as much as Egypt to my eye...

------
dkopi
It's interesting to judge conflicts based on this ranking as well. Check out
#55 (Palestine) and #175 (Israel)

------
simonsmithies
What's wrong with New Zealand?

~~~
jwilk
Longitude overflow.

------
q1t
Dead already :\ hn effect in work

------
laurent123456
The UK map, unlike France or Spain, doesn't include the oversea territories.

------
simonsmithies
What's wrong with New Zealand? Looks even tinier than usual in Safari on iOS.

------
JoeAltmaier
Love to see a world map tessalated this way!

