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Is there a map projection (or a more appropriate term) which allows you to see every country as an equally sized land area, but positioned approximately in the correct geographic position?

Water could still be incorporated as it shows continental separation, etc.

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every country as an equally sized land area> You mean all countries have the same area? So say the area of Taiwan is equal to the area of the United States? –  R.K. Feb 9 '12 at 4:02
R.K., yes each country would have the same land area as every other country. –  Gerald Kaszuba Feb 9 '12 at 4:13
What do you need it for btw? The countries won't retain their shapes if you make their areas equal. –  R.K. Feb 9 '12 at 4:49
Some examples of cartograms, including area cartograms (which are the solution here), appear in the thread at gis.stackexchange.com/questions/7406/…. –  whuber Feb 9 '12 at 15:06
Countries will retain their shapes with an exploded cartogram, R.K., and the objective of an area cartogram in general is to keep their shapes recognizable if at all possible. Drawing them all with equal area is unusual, but it is in principle no more difficult than scaling the areas to any other attribute. –  whuber Feb 10 '12 at 0:20

2 Answers 2

up vote 7 down vote accepted

I think you want a cartogram - but you need to decide what attribute you want to set the size of countries by. Population is a usual one but any attribute can be used. See http://www.ncgia.ucsb.edu/projects/Cartogram_Central/types.html for an introduction. I have an example of producing discontinous cartograms with SLD at http://ian01.geog.psu.edu/geoserver/www/cartogram/discontinous.html

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Yes, if you truly want them all to have the same area you can create a cartogram based on a dummy attribute field that contains a value of 1 for every country. –  nmpeterson Feb 9 '12 at 14:54
I think if you set them all to 1 then they would be their usual size. You'd need inverse of area to make them all the same size. –  iant Feb 9 '12 at 14:56
It depends on the software interface, but usually the cartogram works by making the areas proportional to a specified attribute, such as population. Therefore, to obtain equal areas, all values of that attribute must be equal to each other (and positive): nmpeterson's solution is the correct one. –  whuber Feb 9 '12 at 15:04

Just chiming in to agree with @iant's answer and to mention that there is an R package cart that does this (in theory). I haven't found any examples online and the documentation is quite scant.

There is a second R package RCartogram but it also seems to be in quite an early stage of development.

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