Math Formula

Wednesday, December 21, 2011

Nothing Is Ever What It Seems - An Alternate View To The Globe

Recently I was given an atlas as a present by good friends. May not sound too surprising - unless you take into account that this atlas does not represent the world in the way we got used to since we were kids, but in a slightly different format. Something like this (source:

Confused? Maybe even more so if you contrast it with the more traditional world map (source:, combined by the author; click to enlarge):

As you see, some areas on the traditional map (on the right side), appear bigger relative to others, when compared to the Peters map (on the left side), which presents areas exactly in the ratio they actually are. A few highlights of how areas are over-presented in the traditional map (all numbers:
  • Europe appears only slightly smaller than Africa; in fact, it's only one third (10,180,000 km2 vs. 3,221,532 km2)
  • Greenland appears similar to Brazil, whereas actually it's only a quarter (2,166,086 km2 vs. 8,514,877 km2)
  • The three Scandinavian countries Norway, Sweden and Finland combined appear even bigger than Mexico, whereas the very opposite is true (835,216 kmvs. 1,972,550  km)

So, what's wrong here? Well, the problem is, that we are apparently trying to represent a round, three-dimensional ball on a flat, two-dimensional sheet of paper. Kind of similar to squaring the circle, which is known to be rather difficult a task either.

Thus, inherently all representations of the world on a map are wrong.

Each representation is a trade-off between keeping
  • distance equality
  • angle equality
  • area equality
Unfortunately, you can only preserve two, but not all of them (for more background information, please refer to the Wikipedia article on map projection).

Since maps were originally mainly used for navigational purposes, it was rather useful to keep both distance and angle, and disregard area equality. (Just imagine where important sailors like Christopher Columbus, Vasco da Gama, Marco Polo or James Cook might have ended up on their long journeys home without proper cartographic and navigational equipment)

However, this "area inequality" is more severe the closer you come to the poles. Therefore, areas closer to the poles are more stretched and appear bigger relative to the ones around the equator. As it happens, this representation extremely favours areas like the USA and Europe - the western world, at the expense of Africa, Latin America, ...

This is not to blame "westerns" of using a "wrong" map - as I said before, all maps are wrong to some extent. Yet, I think disregarding economic power and political strength, it is fair not to draw any short-sighted conclusions based on a misleading representation of sizes.

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