TheLeadenSea comments on No arguments here

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.

permalink

fedilink

source

parent

[–] NateNate60@lemmy.world 2 points 1 year ago (3 children)

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

permalink

fedilink

source

parent

hideshow 3 child comments

[–] supernicepojo@lemmy.world 4 points 1 year ago

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

permalink

fedilink

source

parent

[–] Eatspancakes84@lemmy.world 2 points 1 year ago (1 child)

Counterexample: North and Southpole on Earth.

permalink

fedilink

source

parent

hideshow 1 child comment

[–] SparroHawc@lemmy.zip 1 point 1 year 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.

permalink

fedilink

source

parent

[–] Snazz@lemmy.world 2 points 1 year ago

This shape could exist as a projection onto an upright cylinder, wrapping around the cylinder. The two straight edges go vertically along opposite sides of the cylinder. The curved lines wrap around the circumference. The lines are now straight and parallel on the net of the cylinder.

But we can go further: Imagine taking this cylinder and extending it. Wrap it into a loop by connecting the top to the bottom so it forms a torus (doughnut) shape. This connects both sides of the shape, now all “interior” angles are on the inside of the square, and all “exterior” angles are on the outside. The inside and outside just happen to be the same side.

permalink

fedilink

source

parent