Mobius strip Knot Diagram Extended Gauss code Braid Theory 15.01.09

A clockwise 3 flip mobius strip can be cut down the middle, then given a crossing number of 6 to become a knot diagram with extended gauss code or even a braid. How does a looped plain with trefoil knot and three self loops, equal the same looped plain, that is a figure of eight knot with only two loops. When the paper crosses itself, it cancels 2 twsits in the loops, but the two knots don't add up?

Category:

Science & Technology

Tags:

• mobius
• strip
• topology
• knot
• braid
• gragh
• trefoil
• figure
• of
• eight

[kitefrog]

Thanks. At 2:35 I didn't mean that they are the same. I just meant that they share both a none alternating figure of eight knot.

group one: none alternating figure of eight knot with two loops

group two: a trefoil knot with three loops.

group three: is special, it has a none alternating figure of eight knot, two loops but can for a braid as seen in the video start.

[kapazas2002]

betti number

[multidstringtheorist]

That's a hell of a note book... look at the Prime number chain... look at the patterns in clumps of 8 or 16 digits and transpose up the chain.. you're saying things add up that dont.. a -1,-1,-1,1,1,1,-1 isn't the same as -1,-1,-1,-1,1,1,1,1, its sequenced by you.. its under your nose.. you wrote the diagrams... look at them.. good luck..MtD

[multidstringtheorist]

you were saying it didn't add up.. it does! its right in front of you.. look at your number sequences Vs the various knots not counting the ones with half cuts and look at the way the pattern migrates.. I've only seen this once and i'm going to look again... hope you see it..

MtD

[multidstringtheorist]

You need to figure out an algorithmic key.. you could be complicating things with the half cuts...you lost me there for a while.. i kept thinking the predictability of the Fibonacci sequence could be used as a barometer to the gauss? code you're using for your number sequence...

MtD

[onemouseable]

when you reduce the loops out... through the video... the first one is like uo... uo...

the second one is uo... ou... (the one which ends in four u contiguously)

while you factor out the loops, does the orientation of the loop not matter?

Don't know why it should, and here the case is simple, please try looking at this in detail for more complex cases.

I smile at your work! Nice!