Geometrical shape

[4legsgood]

If you take a strip of paper or pliable material and twist it once, then join the ends thus producing a shape that appears to have only one continuous plane and one continuous edge, what is its name. Am I correct in believing that it cannot be carved from a solid block or a mould (or its solidifying liquid content) be created? Also is there any simple literature or web site regarding this strange shape e.g. in the creation of the universe and the laws of science.

[factor-fiction]

mobius strip

[Jumbuck]

Möbius strip (can also be spelt Möebius)

[4legsgood]

Many thanks to you both. Can it be carved or moulded? I believe not.

[factor-fiction]

Is this a 'leggy/legend' wind-up?

[4legsgood]

Sorry factor30 - don't understand your remark. I am of the belief that a mobius strip can only be produced by joining the two ends together and can't be made in a solid form as a unit without a joint because it has only one plane and edge.

[fo3nix]

No, it can be made just fine.

Also, lookup Klein bottle.

[Huderon]

If you were a really good sculptor or woodcarver it might be possible to carve one - after all it is just a 3 dimensional shape.

As for moulding ... There is a very old technique called lost wax casting. You could make a strip from a nice thick strip of wax, put a sprue on it and use the method to create a mould. You'd have to burn the wax off and replace it with metal and then remove the sprue and clean up the resulting strip, but it could be done. I've also come across a page showing photos of knitted and croched strips, and a couple of pages with photos of Mobius earrings. And if you haven't come across them before, trihexaflexagons are also Mobius strips.

In real life a Mobius strip does have practical applications, a Mobius resistor is one.

[Huderon]

oops ... That should have been trihexaflexagons ... sorry about that, it's the small point size stopping me from reading what I wrote properly

[4legsgood]

Thank you both fo3nix and Huderon especially for the references to similar shapes. Not being a mathematician or scientist I find it hard to understand the possibility of a continuous inside/outside naturally formed structure that has no jointed or other artificial connection of the ends. I have seen examples of knitted mobius strips but these are not true/pure strips as they have loose ends which are not connected or have been knotted. I think I understand the lost wax mould construction. So tomorrow a block of cheese will dissapear from the fridge to see what happens when I carve it up albeit with rough crumbly surfaces, should taste nice!!

[Huderon]

If you Google "Mobius strip topology" you will find within the first two pages of results, a reference to an 2004 article where Japanese scientists managed to get a crystal to form a Mobius strip. I wouldn't think it too likely to happen naturally though.

Basic information about it is available at http://www.bbc.co.uk/dna/h2g2/A337592
There is a piece written by a guy who knitted one from the edge (a seamless one) at http://web.meson.org/topology/mobius.php ... there are also photos of some other knitted and croched items there too
A photo and brief description of a music box using one is at http://blog.makezine.com/archive/2009/08/mobius_strip_music_box.html?CMP=OTC-0D6B48984890 /> And finally .. how about a building ? Have a look at http://www.neatorama.com/2009/08/27/a-building-shaped-like-a-mobius-strip/

[R1Geezer]

This was done to death some weeks ago. A mobius strip is a 3D representation of a 2 shape, it has some thickness so it has more than one edge. The paper version is just a represenation. To have the properties you describ the paper would have to be 0 thick which it isn't. Similarly draw a square on a peice of paper, now cut it out, is it a square? no it's a cuboid, all be it a very thin one! The mobius strip could be carved out of a solid block of whatever,if the precision was available but like the paper one above it won't have one face and one edge because it will only be a 3d representation of one.