[Turtle]

Originally Posted by Turtle

Now I don't know about other shapes yet, but I have a bit more on the Möbius strip. As one approaches the length/width limit of , the Möbius strip gets flatter & flatter, but it is possible to flatten down the other springy strips as well. Doing this to a particular Möbius ratio gives a regular hexagon, and I suspect the width then is 3* . (For my 16 /3/4" length, if I cut a strip ~3 1/4" wide & make a Möbius strip of it, that strip will flatten into a regular hexagon.)

Now for my wild speculation>>> The Wicki article I linked to says this at the bottom:

Then we have a recent report here on a strange hexagon at Saturn's North pole >> http://hypography.com/forums/space/1...Saturn+hexagon

My speculation is that we see a hexagon, but it's really a Möbius strip of charged particles.

Here's a scan of my 16 3/4" X 3" Möbius strip partially flattened and forming a regular hexagon.

[Jay-qu]

Originally Posted by Turtle

Then we have a recent report here on a strange hexagon at Saturn's North pole >> http://hypography.com/forums/space/1...Saturn+hexagon

My speculation is that we see a hexagon, but it's really a Möbius strip of charged particles.

Better call NASA, Turtle accidentally did their job again..

[Turtle]

Originally Posted by CraigD

Short, wide Mobius strips seem kinda ugly and clunky. I wonder if any objective “looks like a pretty Mobius strip” criteria can be stated?

All Mobius strips made of twisted rectangles, even long, thin ones, are slightly kinky. I wonder it one can make a kink-free strip out of a flat, non-rectangular shape?

Ugly ‽ Clunky‽ I get the sense you are prodding this ol' turtle‽

Very well; I'll assume the role of umbrage taker. Möbius strips of all proportions are not kinky, only half-twisted, and objectively simply beautiful. Moreover, as a family where the length is held constant while the width varies, the beauty is compounded at the for each additional member. Tooooo sexxxxy!!

The kink-free business from a flat non-rectangular shape sounds like a subject for a thread on topology in general. A Klein bottle perhaps? At any rate, not a Möbius strip, so back to them.

Having covered the surface itself a bit, I have in mind to poke about in the hole a Möbius strip bounds. What shapes can the hole assume? Can you pass one Möbius strip through the hole of one equally proportioned? For the same question, does it matter if the twin is of opposite hand? What are the limits for passing Möbius loops of a single family through one another? Can they get stuck together?

Originally Posted by JayQ

Better call NASA, Turtle accidentally did their job again..

Only one caveat; I did it on purpose. It's what we generalists do. To quote Roger Thelonious George, "chaos favors the prepared imagination."

[Turtle]

Originally Posted by Turtle

Now for my wild speculation>>> The Wicki article I linked to says this at the bottom:

I tried to find this article, but it appears the IEEE archive is for paying folk only.

Originally Posted by wicky

A device called a Möbius resistor is an electronic circuit element which has the property of cancelling its own inductive reactance. Nikola Tesla patented similar technology in the early 1900s: U.S. Patent 512,340 (patent link) "Coil for Electro Magnets" was intended for use with his system of global transmission of electricity without wires.

This is an interesting design, but I don't quite yet see why it is Möbius. For some reason I can't get to the drawing again!???

I think I'll make some nested strips.

[freeztar]

Originally Posted by Turtle

Then we have a recent report here on a strange hexagon at Saturn's North pole >> http://hypography.com/forums/space/1...Saturn+hexagon

My speculation is that we see a hexagon, but it's really a Möbius strip of charged particles.

Quite an interesting proposition Turtle. The only problem I see right away is that the angle from the JPL site photo is not from directly above the north pole. I suppose it doesn't matter if the Mobius belt is in an extremely compressed state (ie occupies a thin layer of atmosphere). The JPL site also states that the hexagon was far lower in the atmosphere than they expected it to be: "The new images taken in thermal-infrared light show the hexagon extends much deeper down into the atmosphere than previously expected, some 100 kilometers (60 miles) below the cloud tops. A system of clouds lies within the hexagon. The clouds appear to be whipping around the hexagon like cars on a racetrack." - JPL. I'm not an astrophysicist, but it seems to me, logically, that a Mobius belt would form high in the atmosphere. Even if you consider the circular motion about the pole and a potential magnetic vortex, the Mobius belt would still have to be isolated in a relatively thin atmospheric layer. I'll admit to not knowing much about magnetic fields, so perhaps I'm overlooking something basic here.

How can the "Flattened-Mobius-Hexagon Speculation" explain the photo (and video)?

[Jay-qu]

When you cut a mobius in half (long ways), you get a sort of double mobius happening - whats more interesting is if you then cut that in half you get 2 double mobius' but linked together!

[Turtle]

Originally Posted by Jay-qu

When you cut a mobius in half (long ways), you get a sort of double mobius happening - whats more interesting is if you then cut that in half you get 2 double mobius' but linked together!

Aye maty; but we'll not be puttin' me family to the shears I'll be tellin' yer.

Originally Posted by freeztar

Quite an interesting proposition Turtle. The only problem I see right away is that the angle from the JPL site photo is not from directly above the north pole. I suppose it doesn't matter if the Mobius belt is in an extremely compressed state (ie occupies a thin layer of atmosphere). The JPL site also states that the hexagon was far lower in the atmosphere than they expected it to be: "The new images taken in thermal-infrared light show the hexagon extends much deeper down into the atmosphere than previously expected, some 100 kilometers (60 miles) below the cloud tops. A system of clouds lies within the hexagon. The clouds appear to be whipping around the hexagon like cars on a racetrack." - JPL. I'm not an astrophysicist, but it seems to me, logically, that a Mobius belt would form high in the atmosphere. Even if you consider the circular motion about the pole and a potential magnetic vortex, the Mobius belt would still have to be isolated in a relatively thin atmospheric layer. I'll admit to not knowing much about magnetic fields, so perhaps I'm overlooking something basic here.

How can the "Flattened-Mobius-Hexagon Speculation" explain the photo (and video)?

To the pink, I reason that 'they' were surprised because they are not looking for a electro-magnetic Mobius band, but rather thinking in terms of clouds & fluid dynamics.

To the bold & the rest, the Saturn Mobius band is thin indeed, but not paper thin according to my new calculations. Lacking a micrometer, I measured a stack of 38 sheets of my 32 lb paper at 5/16" and calculated a mean thickness of .016447368". Then, I calculated the maximum diameter of the 3 wide x 16/3/4 long hexagon forming Mobius strip when it is completely flattened at 7.4". Next, I took the ratio of 2 thickness' to diameter and found it .0022222617.

Now taking the ratio of thickness to diameter from Saturn's hexagon Mobius band we have 100km thick by 25,000km diameter, for a ratio of .004. This is twice that of the paper.

Then again, as you point out about the perspective, we can't tell if the hexagon is curved or flat. I don't know enough about magnetic fields either to say exactly how this works, and sorry to say it seems we gotta pay for that knowledge. I say, we storm the archive & take some booty. Ar ye wi' me mates!!??

[CraigD]

Originally Posted by Turtle

Then we have a recent report here on a strange hexagon at Saturn's North pole >> [ ”Hexagon on Saturn” and ”Cassini Images Bizarre Hexagon on Saturn” ]

My speculation is that we see a hexagon, but it's really a Möbius strip of charged particles.

I can’t see how an image produced by swirling gas can be equated to a Mobius strip, other than by a superficial resemblance.

The Saturn hexagon appears to be a cloud and gas formation. It’s not a true object in the sense that that an ordinary Mobius strip is. While the latter is made of a thin rectangular solid comprised of a bunch of atoms bonded into molecules, stuck together into cells, which are stuck together into fibers, which are stuck together into the thin sheet, the Saturn “hexagon” is a bunch of atoms and molecules in gas form, some likely clumped into dust/smoke particles, but not a solid whole. Matter is constantly entering and leaving the formation, and moving within it. It’s no more really a “band” than are the various bands of Saturn’s rings, or a procession of cars on a busy highway is a “snake”.

Another problem with drawing an equivalence between a Mobius strip and Saturn’s hexagon is that the latter’s not shaped much like a strip of paper. Though overall shaped like a thin band with 6 somewhat strait segments and 6 sharp angles, the segments vary a lot in thikness, from about 100 to 1000 km in width. Observations have revealed them to extend about 100 (but not as much as 1000) km from their tops to their bottoms. Their shape, then, appears to be roughly that of a flattened cylindrical tube, with no sharp edges to allow them to be divided into a top and bottom face for the Mobius construction to make a single surface. Scrutinizing the JPL images reveals no sign of the (single) distinct edge that defines a Mobius strip. In short, it’s hard to make a decent Mobius strip out of a garden hose – especially one that’s made out of wind and clouds.

The Mobius strip analogy might be more applicable if the wind direction within the Saturn formation showed a distinct pattern of alternating up and down at adjacent sharp corner (under high magnification, the corners don’t appear all that sharp, with radiuses of at least a couple of tens of kilometers, but still, clearly, a lot of air is changing direction more abruptly than usual). This would indicate that the formation was in a sense “folded” rather than curved. Visual examination of the images doesn’t appear to suggest this, and, AFAIK, Cassini’s instruments capable of imaging this don’t include ones capable of directly measuring wind velocity (eg: doppler radar). It’s imaging radar is, I believe, intended for surface mapping, not velocity measurement – though it’s unwise to underestimate the flexibility with which mission staff – some very smart folks - can use their instruments.

What’s forming Saturn’s strange “hexagon” is a fascinating mystery, on a par, I think, with that of Jupiter’s Great Red Spot. We’ve got to be careful to avoid finding patterns that aren’t really there, however – the human brain seems optimized to finding such patterns, even when it must be excessively inventive to do so.

[Turtle]

Originally Posted by CraigD

I can’t see how an image produced by swirling gas can be equated to a Mobius strip, other than by a superficial resemblance.

...What’s forming Saturn’s strange “hexagon” is a fascinating mystery, on a par, I think, with that of Jupiter’s Great Red Spot. We’ve got to be careful to avoid finding patterns that aren’t really there, however – the human brain seems optimized to finding such patterns, even when it must be excessively inventive to do so.

That you (or 'they') can't see how, does not affirm that my conjecture is false. We've got to be careful not to discount explanations simply because they don't come from a 'specialist'.

Imagine if you will, in your best gedanken style, a rain storm at night and you turn on a spotlight which you slowly rotate through the sky. The apparent motion of the beam has nothing to do with the motion of the rain drops, which continue to fall whether they're in the light or not. I see the hexagon on Saturn in a similar light, in that the magnetic field is the light and charged particles in the atmosphere are the drops. They only 'glow' when they're in the path.

Anyway, discounting my conjecture seems to require more than casual objections.

PS Let's not forget that we have a source stating that charged particles doform Möbius bands in Earth's atmosphere. I can't find the actual article, but here is the reference Wicki gave:

Originally Posted by wicki

Charged particles, which were caught in the magnetic field of the earth, can move on a Möbius band (IEEE Transactions on plasma Science, volume. 30, No. 1, February 2002)

PPS I just sent an e-mail to the webmaster at SpaceWeather.com with my conjecture and a link to this thread. We might as well get this over with.

[Qfwfq]

Originally Posted by Turtle

Whether by paper or by gedanken, you have given the exact value I asked for, and it agrees with my result; Nicely done!

And yet I can make one with length equal to width plus overlap, that is a perfect square if you don't count the overlap. It's the extreme limit case, of course.