Advanced Mobius Strip Topology

[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.

[tortaelpastor]

crystal meth........

[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.

[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?

[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.

[stoat1000]

Did you know that some dna forms itself into rings? Mitochondrial dna does and some bacterial dna. There's also the point that for stability palindromes seem to be important. So maybe use the word "mississippi" make it a palindrome "mississippiippississim". This is written on the rungs of a ladder. on the uprights we need the letters "p" and "s" alternating. the bottom edge will have a "p" on one corner and an "s" on the other. The number of twists has to give us a "p" and "s" at the join.

[shikamarusgirl17]

Wow this is really interesting... I never really thought so much about this kind of thing until now.

[faunflynn]

Curved lines in graph theory make no difference.

For non planar graphs you could simplify with chromatic numbers.

bye the bye this has all been done before.

But this is good work.

Great post.

[lisinka3]

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

[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.

[jebus733]

you say "um" alot xD. But i really like you for your hard work. I some day wanna study math (only in gr 12)

[Knukleheada]

my brain is hurting

[xp0ferens]

lol @ "paseudo"

[oligiscool1]

why are you doing this? i ask because you don't appear to be a mathematician.

[maths486]

you don't need to be a mathematician to do or appreciate mathematics. mathematics is for everyone.

[oligiscool1]

i suppose that is true...but i know mathematicians (phD level, set theory guys) who aren't even this carried away by topology.

i mean, to each his own. i am probably biased in my view being an engineer, so i can't really see past doing something potentially tedious if there is no clear benefit.

in any case, well said. i withdraw my argument...

[steve9340]

How can I view your Mobius strip videos starting with the first one?

[kitefrog]

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

[cgibbard]

I hit the character limit, but I was going to say that the theorem which says that if a graph can be embedded in the plane with curved lines, then it can be embedded in the plane with straight line segments is called Fáry's theorem so that you could look it up (say, on Wikipedia) if you want. :)

[cgibbard]

Your definition of non-planar is a bit unusual. Normally a graph is called non-planar when there is no way at all to position the vertices such that the straight-line-segment edges connecting them will not cross. (Rather than just the positions you chose for the vertices didn't work out.)

It's possible to show that if there's a way to do it with non-crossing curves joining the vertices, then it's also possible to do it with straight line segments, by moving the vertices appropriately.

[RoyKead]

Anyway, one of the most curious discoveries I noticed was that a two-dimensional object that was deformed in the third, but cut in the second could be wrapped around itself (the knot). I wonder if that's applicable or marketable? You'd sure be quite wealthy if you figured it out, which is always nice...  ;)

Anyway, good luck! Can't wait to see more!

~J

[dr007Orm]

Actually also the other graph (see 3 min 12 sec) is planar...

[999madcows]

kitefrog,

"pseudo" is pronounced "SUDO"

and

"Euler" is pronounced "OILer"

haha :)

nice notebook

[blejanre]

props. I love it when people think about stuff.

[Deciheximal]

Could you please elaborate on the "half snips" process of flattening a mobius strip? When I try it I still get bends so it isn't flat like yours.

[XVIIITheMoonXVIII]

You can only flatten a strip with an even number of twists, as it will have two edges. A strip with an odd number of twists (like to basic mobius strip) cannot be flattened.

[luke1tothe37]

YAY MATH!!!

[luke1tothe37]

Whoa...I thought they were cool, and something that blew up my brain, but...WOW.

PS: Euler sounds like "oiler"

[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.

[Radioheadophile]

Quick question: how old are you?

I mean... topology amazes me (especially concerning higher dimensional objects), but I don't have notebooks of information and such. Am I slacking off, here, or are you older than 20?

[simdude5150]

After watching your videos I decided I wanted to make a flat 3 twist mobius just for giggles. Man that was harder than it looked so good job making all of those.

Why oh why would you throw out the strange 8 intersection one?

Is there some way perhaps to prove that there are a finite number of core shapes and then move from there? I sure don't know how to do it, but I know things like that have been done.

But yeah. Cool.

[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

[reesmaxwell]

At 5:16 in the video you talk about no. 8 and no. 28 being mirror images, and yet your binary notation shows no. 8 being 111100110000 and no. 28 being 000110001111. These are not mirrored.

It is interesting that several are duplicates, with 1 and 22 as one example of that.

Looks like you've been having some fun! Your charts remind me of Wolfram's "A New Kind of Science."

[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?