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[-] supernicepojo@lemmy.world 3 points 1 month ago

Can straight be defined in a nonlinear environment?

[-] Zkuld@lemmy.world 4 points 1 month ago

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.

[-] NateNate60@lemmy.world 2 points 1 month ago

Euclid's first postulate: Give two points, there exists exactly one straight line that includes both of them.

[-] supernicepojo@lemmy.world 4 points 1 month ago

This only applies in 2nd order real space. Euclidean geometry aside, I agree with at least one line could exist between two points

[-] Eatspancakes84@lemmy.world 3 points 1 month ago

Counterexample: North and Southpole on Earth.

[-] SparroHawc@lemmy.zip 1 points 1 month ago

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.

this post was submitted on 08 Jun 2025
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