Every Map You’ve Ever Seen is Radically Inaccurate
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Also imho saying that mercator projection is radically inaccurate is misleading, as it is actually very accurate for some things, which is the reason it's afaik used in navigation.
http://en.wikipedia.org/wiki/List_of_map_projections
See the "Properties" column and description of each at the end. Mercator is marked as "Conformal", which means local angles are preserved. I believe that basically means if you are going 45°, and you draw a 45° line from your current location on a Mercator map, you will end up where that line goes. Which explains why it's so good for navigation.
I can't believe that most people here haven't see the Dymaxion Map: http://en.wikipedia.org/wiki/Dymaxion_map