This whole post is a good illustration to how math is much more creative and flexible than we are lead to believe in school.
The whole concept of “manifolds” is basically that you can take something like a globe, and make atlases out of it. You could look at each map of your town and say that it’s wrong since it shouldn’t be flat. Maps are really useful, though, so why not use math on maps, even if they are “wrong”? Traveling 3 km east and 4 km north will put you 5 km from where you started, even if those aren’t straight lines in a 3d sense.
One way to think about a line being “straight” is if it never has a “turn”. If you are walking in a field, and you don’t ever turn, you’d say you walked in a straight line. A ship following this path would never turn, and if you traced it’s path on an atlas, you would be drawing a straight line on map after map.
Thank you for the informative answer
This whole post is a good illustration to how math is much more creative and flexible than we are lead to believe in school.
The whole concept of “manifolds” is basically that you can take something like a globe, and make atlases out of it. You could look at each map of your town and say that it’s wrong since it shouldn’t be flat. Maps are really useful, though, so why not use math on maps, even if they are “wrong”? Traveling 3 km east and 4 km north will put you 5 km from where you started, even if those aren’t straight lines in a 3d sense.
One way to think about a line being “straight” is if it never has a “turn”. If you are walking in a field, and you don’t ever turn, you’d say you walked in a straight line. A ship following this path would never turn, and if you traced it’s path on an atlas, you would be drawing a straight line on map after map.