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this post was submitted on 08 Jun 2025
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Can straight be defined in a nonlinear environment?
I would guess on a sphere these can be straight yes: The pole goes into the center of cicular thing and radius of the sphere needs to put the other arc on one latitude.
Euclid's first postulate: Give two points, there exists exactly one straight line that includes both of them.
This only applies in 2nd order real space. Euclidean geometry aside, I agree with at least one line could exist between two points
Counterexample: North and Southpole on Earth.
No, it's still accurate - the straight line goes through the center of the Earth. Only in coordinate systems where 'straight' is defined as following the curvature of a surface are there infinite lines between the North and South Poles... and that would be non-Euclidean geometry.