Möbius strips

[Turtle]

[ATTACH]1486[/ATTACH]

 

 

It reminds me a bit of one of the "petals" of the vesica piscis flower:

 

[ATTACH]1487[/ATTACH]

 

Mmmmm...genetic memory no doubt.

 

 

 

Bhat Wrand? :D :)

 

Inversion from Deschutes Brewery in Southern Oregon. Too soft for me; hoppiness OK; but at 6.8% al-cue-hall, I'd swear out a testimonial in a whip-stitch. :beer: :hihi: :evil: :)

[Qfwfq]

I thought so too; however, using another canvas square 9"x9", I marked off a 7" edge and then puckered and pinned said band banana Möbiusly (Möbius bananally?), i.e. I joined the longest edges. Seems we all were mistaken about the limiting case. :cup: :D :confused:

I had been considering that, for cloth which is more flexible than paper and not elastic, but I reckoned it would imply scrunching up and not just neat folding. Your picture looks neat enough, good work! I'll be trying to figure it out myself.... ;)

 

Of course we're talking about a problem of doing it in 3-D and without improper self-intersections. For instance, embedding a Klein bottle in 3-D has this difficulty but in 4-D you can always go around a surface instead of through it.

[Turtle]

I had been considering that, for cloth which is more flexible than paper and not elastic, but I reckoned it would imply scrunching up and not just neat folding. Your picture looks neat enough, good work! I'll be trying to figure it out myself.... :)

 

Of course we're talking about a problem of doing it in 3-D and without improper self-intersections. For instance, embedding a Klein bottle in 3-D has this difficulty but in 4-D you can always go around a surface instead of through it.

 

Excellento! I am a little unclear on the last paragraph. (OK; very unclear. :lol: ) ) 'Improper self-intersections' has me stymied. As to the 'scrunching up', I had the same impression. I am thinking something more akin to a folding fan. So we come now to the question/problem of just how big a ratio of L/W can be joined on the long edge. :)

 

In the mean time, I do have in mind to sew up a Klein bottle as soon as I buy some more fabric. :phones:

[Qfwfq]

as soon as I buy some more fabric.

For a Klein bottle, make sure you get a very, very lacey fabric. ;)

[CraigD]

I thought [that the unjoined edge of a rectangular piece used to make a Mobius strip could not be shorter than its joined edge] so too … Seems we all were mistaken about the limiting case. :doh: :D :shrug:

Yes, we were.

 

All of these mistaken edge length ratios limits – [math]\sqrt3 : 1[/math], [math]1 : 1[/math] - seem to result from assumptions about what sort of folding is allowed. When any sort of folding is allowed, any ratio is possible, subject only to the physical limitations of the material being used.

however, using another canvas square 9"x9", I marked off a 7" edge and then puckered and pinned said band banana Möbiusly (Möbius bananally?), i.e. I joined the longest edges

I’m able to make a paper Mobius strip using by folding the paper an even number of times (\/\, \/\/\, etc, not \/\/), then twisting and joining the flattened, multi-layer strip in the usual way, \/\ edge to \/\ edge. The more folds are made, the more the resulting Mobius strip looks like a “normal” one (from a distance).

I am thinking something more akin to a folding fan.

With many folds, the paper does look a lot like the sort of fans kids make while bored in class, etc., until twisted and the ends joined.

So we come now to the question/problem of just how big a ratio of L/W can be joined on the long edge. :eek: :)

.From ordinary sheet of paper, I was able to make a mobius strip from a 2.5” x 10.75” piece, with about .5” of overlap, for a ratio of better than 1:5. Doing much better would be an exercise in paper selection and folding technique.

 

Here are the efforts of my labor:

From left to right, 8:10.75 with 2 folds, 8:10.75 with 4 folds, and 2:10.75 with 18 folds (with no attempt to apply tape!)

 

Of course we're talking about a problem of doing it in 3-D and without improper self-intersections. For instance, embedding a Klein bottle in 3-D has this difficulty but in 4-D you can always go around a surface instead of through it.

I am a little unclear on the last paragraph. (OK; very unclear.:doh: :hyper: ) ) 'Improper self-intersections' has me stymied.

…

In the mean time, I do have in mind to sew up a Klein bottle as soon as I buy some more fabric. :cup:

For a Klein bottle, make sure you get a very, very lacey fabric. ;) :cup:

What I think Qfwfq is getting at about improper self-intersections and the need for very lacey fabric is that, in 3 dimensions (all we’ve got to build actually naked-eye stuff in), the surface of a Klein bottle isn’t actually a single surface with no edge, because of the need for a “hole” to allow the tube from which its formed to pass through its own surface to get from the inside to the outside of the bottle. Most Klein bottle makers just make a circular hole to (no pun intended) circumvent this problem (eg: this pretty glass one), but a skilled and so inclined knitter, lacemaker, or weaver could manage it by having the thread/yarn interlace (again, no pun, really! :)) at the circular point of self-intersection.

[Turtle]

For a Klein bottle, make sure you get a very, very lacey fabric.

 

 

Well, I'm goin' with the canvas as I need it for other projects and it's cheap. My plan is to cut a round hole and bind over its edge with stitching so it doesn't fray and then shove the appropriate bits through. What kind of stuffing should I fill it with?

 

I stiched on the long edges a 10"L/5"W Möbius strip yesterday. It is difficult to flatten and it hasn't flattened into any nice geometric shape. I can't reach into some of the interior folds which are coiled inside other interior folds.

[Qfwfq]

What kind of stuffing should I fill it with?

Highly viscous stuffing! ;)

[Turtle]

All of these mistaken edge length ratios limits – [math]\sqrt3 : 1[/math], [math]1 : 1[/math] - seem to result from assumptions about what sort of folding is allowed. When any sort of folding is allowed, any ratio is possible, subject only to the physical limitations of the material being used.I’m able to make a paper Mobius strip using by folding the paper an even number of times (\/\, \/\/\, etc, not \/\/), then twisting and joining the flattened, multi-layer strip in the usual way, \/\ edge to \/\ edge. The more folds are made, the more the resulting Mobius strip looks like a “normal” one (from a distance).With many folds, the paper does look a lot like the sort of fans kids make while bored in class, etc., until twisted and the ends joined..From ordinary sheet of paper, I was able to make a mobius strip from a 2.5” x 10.75” piece, with about .5” of overlap, for a ratio of better than 1:5. Doing much better would be an exercise in paper selection and folding technique.

 

Here are the efforts of my labor:

From left to right, 8:10.75 with 2 folds, 8:10.75 with 4 folds, and 2:10.75 with 18 folds (with no attempt to apply tape!)

 

Nice work Craig! And you said you weren't handy with paper. :hyper: I had to do a double take on the photo to find 1:5, but on seeing it I admit you have out-folded me. :hihi:

 

What kind of stuffing should I fill it with?

 

Highly viscous stuffing!

 

Roger Wilco I think I will try honey first. :eek:

[Turtle]

thinking about Möbius electromagnets & why they're special. is that one coil levitating? the grand pooba has seen fit to have me stumble onto about 800 feet of coil wire in 2 different gauges that once saw service as coils on crt's. :evil: :doh:

 

Patent 512,340

In carrying out my invention it is to be observed that certain facts are well understood by those skilled in the art, viz: the relations of capacity, self-induction, and the frequency and potential difference of the current. What capacity, therefore, in any given case it is desirable to obtain and what special winding will secure it, are readily determinable from the other factors which are known.

 

What I claim as my invention is:

 

1.A coil for electric apparatus the adjacent convolutions of which form parts of the circuit between which there exists a potential difference sufficient to secure in the coil a capacity capable of neutralizing its self-induction, as herein before described.

 

2.A coil composed of contiguous or adjacent insulated conductors electrically connected in series and having a potential difference of such value as to give to the coil as a whole, a capacity sufficient to neutralize its self-induction, as set forth.

 

 

http://hypography.com/forums/physics-mathematics/11905-charge-explained.html

[jungjedi]

So I set to twiddling my 1 / 1 canvas Möbius band, and I decided to jam my hand in and see if I could get it on my wrist as a bracelet. My hand is a little too big, but low & behold in the process I jammed that little pecker right into Craig's described form. Well, a cone at first, long & tapering with a sort of tail, but when I flattened it there was Craig's directions and in the form of a 45/45/90 triangle no less! No small coincidence the cone form makes a great dunce hat

 

 

or a mexican hat