| I've cut a 3 flip mobius counter clockwise strip down the middle using special mobius paper that I created. I then added half cuts to the plain so they can intersect for the purpose of getting rid of all twists. As you know, the resulting loop has 8 twists, a trefoil knot and two boundaries (surfaces), but it takes 6 lines to kill the 8 twists. The resulting paper soultion is then put on a page and turned into a knot diagram and knot notation. The knot diagram is then turned into a pseudograph consisting of vertices, lines (I meant to make them straight but I do this in my head) and loops. The findings are very very interesting! All the solutions have a knot crossing number of six (except for one so far - it had 8?), all pseudographs have a network Betti number of 7 and almost all the pseudographs have a Euler characteristic of 0. The original uncut mobius strip has a Euler number of 0! WOW. I think all of these findings are reproduceable and original because I cannot find any related papers so far. Can anyone help? |
