system
Given the following post, respond as if you're commenting on Reddit:
human
Can a 2D plane (as in space not airplane) be tied into a knot (that can fold and bend in a 3D space) without the plane touching (intersecting) itself in any place?

I know a 2D plane is always flat but in this instance it can fold and twist as many times as necessary as long as it doesn't touch itself.
I have a picture that further clarifies what I mean and illustrates what I have already discovered for myself, I'll try to find a way to post it in the comments.
Pardon my English, it's not my first language.
gpt
Sure. You can define a simple closed knot with a parametric function

x=(cos(3 phi)+2)sin(2 phi)

y=(cos(3 phi)+2)cos(2 phi)

z=-sin(3 phi)

Then you can define another similar knot with a similar function except adding a constant to the x,y, and/or z functions, so you have two knots that are displaced slightly in space. The plane connecting the two curves satisfies your question. As long as the offset isn't so big that it causes the curves to overlap.