I’ve seen this meme a couple times in my life, and never understood what “non-orientable” means. The word seems to imply the shape can’t be oriented, i.e. rotated in space, which a klein bottle certainly could be right?
“Non-orientable surface” is the thing. The surface of that thing is not orientable. That means you can’t draw some normal vector to define the surface. When you traverse through the surface with a normal vector you can end up in the same point with that vector pointing the opposite direction in such a surface. That gives two directions for the same point or in other words you can’t define the surface like that with a normal vector. Its the surface and not the shape itself that is non-orientable
If you follow the surface with your finger, starting from the outside, you can end up on the inside, without traversing the surface. There is only one surface, no concept of outside or inside, contrary to a good old cube for instance.
Similar to a Moebius strip but with a higher dimension. A MS is easier to understand since you can easily make one to try to run your finger on the surface and end up anywhere.
I’ve seen this meme a couple times in my life, and never understood what “non-orientable” means. The word seems to imply the shape can’t be oriented, i.e. rotated in space, which a klein bottle certainly could be right?
Can somebody explain?
“Non-orientable surface” is the thing. The surface of that thing is not orientable. That means you can’t draw some normal vector to define the surface. When you traverse through the surface with a normal vector you can end up in the same point with that vector pointing the opposite direction in such a surface. That gives two directions for the same point or in other words you can’t define the surface like that with a normal vector. Its the surface and not the shape itself that is non-orientable
thanks this is the only answer I understoo!
Thanks to everybody else tho appreciate it
If you follow the surface with your finger, starting from the outside, you can end up on the inside, without traversing the surface. There is only one surface, no concept of outside or inside, contrary to a good old cube for instance.
Similar to a Moebius strip but with a higher dimension. A MS is easier to understand since you can easily make one to try to run your finger on the surface and end up anywhere.