Comment on xkcd #3077: de Sitter
Bumblefumble@lemm.ee 1 month agoTry drawing a triangle on a globe and measure the angles, it will be more than 180 degrees. That’s probably the simplest visualisation possible.
Comment on xkcd #3077: de Sitter
Bumblefumble@lemm.ee 1 month agoTry drawing a triangle on a globe and measure the angles, it will be more than 180 degrees. That’s probably the simplest visualisation possible.
idiomaddict@lemmy.world 1 month ago
Look at you, making it all easy to understand
knightly@pawb.social 1 month ago
Spheres are examples of surfaces with positive curvature. Negative curvature (where the angles of a triangle add up to less than 180 degrees) is represented by this saddle shape:
Image
Hamartiogonic@sopuli.xyz 1 month ago
If you draw a triangle on different parts of a toroid, would you get different angles?
knightly@pawb.social 1 month ago
Yup! That saddle is a shape of constant negative curvature. On a toroid, the inside of the hole would have negagive curvature and the outside would have positive curvature.
WalrusDragonOnABike@reddthat.com 1 month ago
Same is true for a sphere. For example, if you draw a triangle with 1 vertex at the north pole and the other two on the equator, all the angles are 90 degrees. But if you move, say, the north pole vertex to be closer to the two in the equator, then you’d get a smaller sum.