Advanced Mobius Strip Topology

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?

Category:

Science & Technology

Tags:

• Advanced
• Mobius
• strip
• Topology
• Pseudograph
• knot
• theroy
• diagram

[kitefrog]

it was a mistake, I pulled a length to far, beyond where it needed to go. it just happened to become symmetric and I got drawn in by its beauty? you are right, very observant, try to re-create it and see what knot it should really be?

[kitefrog]

Thanks Jebus733. You're right about the Umm, I stopped it all togoether in subsequent videos. Look up query you tube 'mobius transformation', and 'turning a sphere inside out'. amazing math videos.

[kitefrog]

thanks, yes I was inaccurate at that time. I understand now. David

[kitefrog]

I'm 36, and Bipolar. I was in Canada this past May 08' and got teaching my 5 yr old niece how to make a mobius strip, cut it and understand the results. This was the start of a manic period that lasted about 6 weeks because when I returned to the UK, pushed this work further, sometimes doing it up to 10 hours none stop. It took me for example 10hours to make all the paper solutions for the one flip mobius strips.

[kitefrog]

yes yes, very true. I've often posted findings a little prematurely. I noticed that error afterwards. They are almost identical, but the loop mutates to a slightly different position and seems to frame shifts the knot notation or just alter it. I've also got A new kind of science.

I suspect there might be up to a hundred or more paper solutions, as you may know counting the resulting Eulerian paths is an open problem in mathematics. thanks

[kitefrog]

Gosh I said Ummm several times. However, I didn't reherse it and made it up as I went. I suspect the Ummm's gave me time to think? Anyone with some ideas?

[lisinka3]

Wow, so dedicated to Mobius strips. I hope you find what you're looking for.

[tortaelpastor]

crystal meth........

[ArtFenerty]

Makes me wonder if your math could have some connection to chemistry and the way various molecules bind.. your graphs look almost like a molecular binidng pattern of the various atoms involved.. curious. Geat work! I love to see such pure research for the heck of it. Interesting things lead to interesting discoveries..

[lornathomas1]

Disappointed you binned the beastie...

[RockMyPartyKesha]

I love möbius strips as well, but not that much.

[Tikeslar]

Your definition of a planar graph is wrong

[tyniehawk]

I'm not sure what significance these have but I enjoyed seeing all the work. YAY FOR DISCOVERY! Also must say I see from your comments below the, like any real scientist, you accept error and can move forward.

[MrTanookiMario]

Did you ever find out anything about the one with a knot crossing number of 8? I'm curious if you made a mistake, or if something more could come of that.

[Ihatebrendon]

too much coffee

[PeeteyP]

Wow, I wanna say wow about this vid , love those sketch books, and I've done Mobius first and second cuts, and like your "library" of mobius dissections.