i posted this on the main guild forum before i realized that there was a special math subforum. i hope im not breaking any rules. if i am, its cuz i didnt know they were there.

I've been wondering about the following question because i design "celtic knots" and have not come across a case where whatever stated below didnt work.

let us define a celtic knot as a design where each piece of rope has the alternating pattern of going under and over and under and over etc... another piece of rope.
You may have just one rope looped together but they still must have the alternating pattern of over under over under. An example of that is a trefoil.
you can have multiple loops wound together too, like an interlocked star of david.
However, the ropes in the design doesnt neccesarily have to be looped together.


can you prove that if you randomly draw a jumble of lines so that the ends of the lines lie in the same loop (or "on the outside" but in topology, the "outside" itself is a loop), you will ALWAYS be able to keep that alternating over/under pattern for ALL the ropes involved in the design?

maybe the proof is simple. i made a really complex case by case one that i dont think even works.