4 ms·

> The shortest path between two points is a straight line uh?

abraves10001 10y ago
Right?! Even on maps it is true. It doesn't mean that there is a viable route on that line or that that line is the preferred one. That one is really bad, imo
- maxerickson 10y ago
  It's only true on certain maps. https://courseware.e-education.psu.edu/projection/chapter9.html https://courseware.e-education.psu.edu/projection/chapter9.h... For regional maps it doesn't particularly matter, the map will be in a projection that has relatively minimal error, but a straight line in most projected coordinate systems will not be the shortest path between those points.
- jcranmer 10y ago
  Depends on the map projection. On the surface of a sphere, the shortest distance between two points is along a great circle route (which is the equivalent of a line in spherical geometry). Polar map projections preserve straight lines as great circle routes, but, e.g., Mercator projections do not. If you're looking at a 5 km × 5 km topo map, the difference isn't particularly significant. If you're looking at a map of Europe or the United States, it is (note that many airline routes seem to follow curved lines--it's because the shortest distance is that curved line).
- ska 10y ago
  Even on maps it is true. That really depends on your map. Or rather, your projection. Which is sort of the point.
deleted 10y ago
[deleted]
deleted 10y ago
[deleted]
Swizec 10y ago
Triangle with 3 right angles. Geometry is weird. https://www.quora.com/How-can-I-draw-a-triangle-with-three-90-degree-angles-on-a-sphere https://www.quora.com/How-can-I-draw-a-triangle-with-three-9... Also, taxicab geometry: https://en.m.wikipedia.org/wiki/Taxicab_geometry https://en.m.wikipedia.org/wiki/Taxicab_geometry
vurpo 10y ago
Depends on your situation. In non-Euclidean geometry (such as on the surface of a sphere, which the Earth approximately is), it's not as simple as taking a straight line between two lines. Also look at Manhattan/taxicab geometry. When you can only move along one axis at a time, you usually can't move in a straight line between two points. Both of these situations have common applications in the real world. For example, in mapping and navigation.

Right?! Even on maps it is true. It doesn't mean that there is a viable route on that line or that that line is the preferred one. That one is really bad, imo

maxerickson 10y ago
It's only true on certain maps. https://courseware.e-education.psu.edu/projection/chapter9.html https://courseware.e-education.psu.edu/projection/chapter9.h... For regional maps it doesn't particularly matter, the map will be in a projection that has relatively minimal error, but a straight line in most projected coordinate systems will not be the shortest path between those points.
jcranmer 10y ago
Depends on the map projection. On the surface of a sphere, the shortest distance between two points is along a great circle route (which is the equivalent of a line in spherical geometry). Polar map projections preserve straight lines as great circle routes, but, e.g., Mercator projections do not. If you're looking at a 5 km × 5 km topo map, the difference isn't particularly significant. If you're looking at a map of Europe or the United States, it is (note that many airline routes seem to follow curved lines--it's because the shortest distance is that curved line).
ska 10y ago
Even on maps it is true. That really depends on your map. Or rather, your projection. Which is sort of the point.

deleted 10y ago

[deleted]

deleted 10y ago

[deleted]

Swizec 10y ago

Triangle with 3 right angles. Geometry is weird. https://www.quora.com/How-can-I-draw-a-triangle-with-three-90-degree-angles-on-a-sphere https://www.quora.com/How-can-I-draw-a-triangle-with-three-9... Also, taxicab geometry: https://en.m.wikipedia.org/wiki/Taxicab_geometry https://en.m.wikipedia.org/wiki/Taxicab_geometry

vurpo 10y ago

Depends on your situation. In non-Euclidean geometry (such as on the surface of a sphere, which the Earth approximately is), it's not as simple as taking a straight line between two lines. Also look at Manhattan/taxicab geometry. When you can only move along one axis at a time, you usually can't move in a straight line between two points. Both of these situations have common applications in the real world. For example, in mapping and navigation.