from a given point on the globe, draw a great circle that runs east-west at the selected point. where does the circle pass through? it is counterintuitive that starting in the northern hemisphere facing (say) east and traveling in a straight line will take you to through southern hemisphere. east or west from European cities, all quite north, might be especially surprising.
in contrast, north-south great circles are lines of longitude, easy to comprehend.
inspired by retroazimuthal map projections.
there is no map projection such that all horizontal lines are east-west great circles. this is a little counterintuitive because in cylindrical projections, all vertical lines are north-south great circles, so it might initially seem some transverse cylindrical projection could work for east-west. however, north-south is different from east-west, because we cannot define an east or west pole: earth's rotation axis matters. also, as noted above, a non-equator great circle passing east-west through a point does not stay oriented east-west along the circle. however, a horizontal line passing through a point on a 2D map projection has to stay horizontal.
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