# Area of countries: Mountains not included?November 19, 2007 4:29 PM   Subscribe

Is topography, relief, or physical terrain taken into consideration when assessing a country's size, or area?

The CIA World Factbook just says "Total area is the sum of all land and water areas delimited by international boundaries and/or coastlines." - but I presume countries with extensive mountain ranges could be have substantially larger area than this point to point method indicates. Is there a list that attempts to rank countries in this way?
posted by takeyourmedicine to Science & Nature (4 answers total) 2 users marked this as a favorite

You'll run into the 2-d equivalent of the coastline problem. Depending on the scale you use, you can get wildly differing amounts.
posted by vacapinta at 4:38 PM on November 19, 2007

This isn't going to be very significant. If you're walking a mile up an insanely steep 50% grade, you are walking 1.1 miles.

If it were a 100% grade (45 degree angle) it would be 40% extra distance.

I doubt even Nepal would gain an extra 5% of its area this way.
posted by aubilenon at 4:45 PM on November 19, 2007 [1 favorite]

Traditionally, the answer is no. In fact, for such things as determining the geographic center of a region, it is assumed to be a mathematically perfect plane, and thus featureless.

You occasionally hear statements about places like Switzerland to the effect "If the mountains could be flattened with an iron it would be one of hte largest countries" (similarly, the Korean Peninsula) but there isn't a standard way to do this so it isn't a formal or serious approach.

Obviously there are ways to weight regions for population or resources and you can see maps of that in various contexts.
posted by dhartung at 4:47 PM on November 19, 2007 [1 favorite]

There is a concept in the mapping sciences called "fractal dimensionality" that describes, if not expressly corrects, the phenomenon you are describing. Basically, if a planar surface has 2 dimensions and a fully-solid tangible object has 3 dimensions, there should exist a range of values between 2 and 3 dimensions to describe the surface in terms of its complexity and form. This paper gives some elaboration on the case that dhartung mentions, common to all mapping endeavors: you must define the scale based on the minimum feature you wish to map. To aubilenon, yes it would only increase 40% extra if it were one 100% grade, but there are cliffs next to valleys, with subtle ridges that jag back and forth... And the rocks are also bumpy... And so are the grains of sand... and so are the molecules... and so on. You could go on forever, but even if you were to stay at the "human scale" of about 2 meters, the area would likely increase drastically. Correcting these topographic effects is a major subject of research (some good, if dated material here).

Now to answer the first question: no, area calculations do not generally take into account these variations in relief. The shape of the earth is now defined by a fixed center point, with direction-specific radii measurements to account for the fact that the earth is just a little less "tall" north to south than it is "wide" from east to west (see Datum). In creating a regional (2d) map, a map projection will hold certain features and distances fixed while approximating others, but distances and areas for calculations are now generally modeled in spherical coordinates around this idealized shape of the earth.
posted by zachxman at 7:58 AM on November 20, 2007 [2 favorites]

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