Location Transport

How does the location of the destinations affect the size of the discrepancy on a globe?

This is about spherical geometry or non-euclidean geometry the prompt was: Discuss why the length of the flight path, of an airplane, from destination A on a paper map. How does the location of the destinations affect hte size of the discrepancy?

Public Comments

1. What kind of discrepancy are you referring to? What kind of map? When making a map of a globe on a flat sheet of paper, there have to some discrepancies, but the map maker can choose a map projection that minimizes the discrepancies in the important variables. http://en.wikipedia.org/wiki/Map_projection http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html If you are sailing on the ocean, you want a map that will tell you which way to steer to get to where you are going. This is what the Mercator projection was designed for. The Mercator projection is designed to cover a band on the sphere. For locations inside the band (even if they are on opposite sides of the world) the angles are accurate (though not optimum). When going by the shortest route in an airplane, the polar projection is what you want. And in a polar projection, the shortest path is accurately displayed no matter how far apart the two locations are. Both of these can distort areas greatly, but the navigators don't care about that. On the other hand, other people need maps that give areas their full due, even if it means that directions are not quite right. Other people care about land areas and not about the oceans, etc. None of this has anything to do with spherical geometry - on a sphere you can have a perfect map of the Earth. The problem comes up when you want to transfer a sphere to a plane