4 ms·

A sheet of paper or a blanket would only be a plane segment.

• grandalf 11y ago
  A string is just a line segment
  • Taniwha 11y ago
    I can imagine an infinitely long line with a know in the middle in 3d ... I guess the interesting question is "can you have an infinite plane with a knot in the middle in 5 dimensions?6 dimensions?"
    • bobbles 11y ago
      if you selected a single point on a plane and pulled it upwards you could then knot it very similarly to a line couldn't you?
      • Taniwha 11y ago
        that's like tieing a knot in a loop of string, not like a granny knot ... I think the sort of knot I have in mind is a harder problem
  • ustolemyname 11y ago
    Yes, but the ends could be extended to infinity in arbitrary directions, so we can tie a knot in a line, not just a segment. You can't do that to the edges of a blanket knot (two sides run into the knot).
    • baddox 11y ago
      A mathematical knot is like a loop of string. There are no ends. Of course, you could cut any mathematical knot wherever you like and make the two ends go to infinity if you'd like.
      • ustolemyname 11y ago
        Thank you, I appreciate the correct definition.
    • OJFord 11y ago
      I understand a bit better after that, thanks. But a knot in a plane segment doesn't need to fold the ends in - I can grab a blanket in the middle, and tie a knot there, then extend edges infinitely still?
  • GFK_of_xmaspast 11y ago
    A knot is an embedding of S1 in R3, i.e. a closed loop and not a line segment.