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> Hence you can't measure real-world distances using string and a paper map.

You very much can. The scale of longitude and latitude is just not the same so you need to do Pythagoras (usually by approximation rules).

There are usually lines to allow for that.



If you only use rigid string and sail in strange curves that map to straight lines in 2d then that's true. Or maybe by "do Pythagoras" you meant to calculate the metric tensor for your projection and integrate that along your shipping route?




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