61. Re: Has A Moebius Strip Spin 1/2? Now what about the moebius strip? Imagine wandering on the surface of such a strip, The connection between spin 1/2 and the moebius strip lives on that http://www.madsci.org/posts/archives/dec98/913299195.Ph.r.html

MadSci Network : Physics Re: Has a moebius strip spin 1/2? Date: Thu Dec 10 04:24:53 1998 Posted By: Georg Hager, Grad student, Theoretical Particle Physics Area of science: Physics ID: 913053558.Ph Message: Dear Ewen! Excellent observation! Although the connection between the rotational properties of spin and a Moebius strip is not as deep as you might have imagined, your question touches some of the most underlying concepts in mathematical physics. I will try to elaborate a bit on the mathematical background, assuming that you are not too well grounded in group theory and topology. Spin 1/2 is a mathematical concept which is often misunderstood. Sometimes people imagine spin as a little `arrow' indicating some axis of `rotation' for an elementary particle. While it is correct that rotation has something to do with it, the connection is more subtle. Physicists describe rotations in space as a certain group, called SO(3). Now you don't really have to understand what a group actually is. Suffice it to say here that it is a set of elements (rotations in our case) and there is an operation which produces out of two group elements another one. This would be two successive rotations about two axes, which can be described as a single rotation about another axis.

62. The City Of Absurdity: David Lynch, Paper The moebius strip subverts the normal, ie Euclidean way of spatial (and, (19) On the one hand, Lacan employs the moebius strip as a model to http://www.geocities.com/~mikehartmann/papers/herzogenrath3.html

On the Lost Highway : Lynch and Lacan, Cinema and Cultural Pathology DIGRESSION 2: HOW TO MAKE A MOEBIUS STRIP Take a strip of paper Make sure that it has two sides Take one end of the strip, make a 180 degree twist, and put it to the other end. Tape - or, better, with respect to suture, which is important, as we will see - stitch the two ends together. As a result, you now have a one-sided figure instead of a two- sided figure. Ill 1: The Moebius Strip The Moebius Strip subverts the normal, i.e. Euclidean way of spatial (and, ultimately: temporal) representation, seemingly having two sides, but in fact having only one. At one point the two sides can be clearly distinguished, but when you traverse the strip as a whole, the two sides are experienced as being continuous. This figure is one of the topological figures studied and put to use by Lacan. On the one hand, Lacan employs the Moebius Strip as a model to conceptualize the "return of the repressed," an issue important in Lost Highway as well. On the other hand, it can illustrate the way psychoanalysis conceptualizes certain binary oppositions, such as inside/outside, before/after, signifier/signified etc. - and can, with respect to

63. Animation Insider - China's "Moebius Strip" Thru the moebius strip turned a few heads when it debuted at the Cannes Film Thru the moebius strip follows Jac s expedition to rescue his father from http://www.animationinsider.net/article.php?articleID=785

64. M.C. Escher And The Moebius Strip Math in the Animal Kingdom, Math @ Home Fun Math Problems for kids and their families. http://educ.queensu.ca/~fmc/december2004/Escher.html

Go Back to the December 2004 M.C. Escher and the Moebius Strip Two strips of paper, about 3cm x 28cm each Sticky tape Two pencil crayons, one blue and one red Place the strips of paper end to end and tape them securely into one long strip. Bring the ends together to form a loop and lightly tape them together. Use the blue pencil crayon to draw a line on the surface of the loop. Keep drawing until you reach your starting point. Undo the tape connecting the loop. Is there a blue line on both surfaces? Using the same strip of paper, give one end a half turn before you join the ends again. You should have a loop with a twist in it. Lightly tape the ends together. The loop is now a Moebius strip Use the red pencil crayon to draw a line on the surface of the Moebius strip. Keep drawing until you reach your starting point. Undo the tape connecting the Moebius strip. Is there a red line on both surfaces? Now, reconnect the Moebius strip and cut along the red line. A Moebius Strip is a surface that has only one surface, as it is attached to itself and twisted halfway around. As you can see in this woodcut by Escher, all nine red ants are on the same side of the Moebius strip!

65. Science Jokes Moebius Strip? Super Sleepers Boron nitride (BN) is the second hardest substance known to man. http://www.sciencejokes.com/science-jokes/index.php?detailed=10718

66. Double Helix Experiments Can you draw on only one side of a moebius strip? moebius strips are often usedas belts in machinery because they last longer – they wear out both ‘sides’ http://www.csiro.au/helix/experiments/dhexpmoebius.shtml

About the Club Hands On The Helix Scientriffic CSIRO's Double Helix Science Club www.csiro.au/helix About the Club Join the Club Member Events ... Contact Us Making a Moebius Strip This loopy structure was invented by a German mathematician named August Moebius. Its amazing properties arise from the fact that this strip of paper has only one edge and one side! Cut a strip of paper 30cm x 5cm (or something like these proportions - it doesn’t need to be exact!) Join the ends to make a hoop, but give the strip a half twist before you tape it together. Draw a line along the centre of the strip. Cut the strip in half along its length. How much bigger is your loop than the one you started with? How much bigger is the loop if you cut the strip into thirds, quarters? Can you draw on only one side of a Moebius strip? Moebius strips are often used as belts in machinery because they last longer – they wear out both ‘sides’ at once. This useful strip is part of a branch of mathematics called topology. Topology can be hard to explain, because it straight lines or edges aren’t important, and a circle is considered to be the same as a square. In topology, one is just a distorted or deformed version of the other! CSIRO's Double Helix Science Club PO Box 225, Dickson, ACT 2602, Australia

67. CEEDC: Culture Explain the history of the moebius strip included with this activity. The students now have a moebius strip. Now, after analyzing the ME strip, http://collections.ic.gc.ca/environmental/culture/ss-striptease.html

Strip Tease Program Area This activity can be used in the Grade 9 Mathematics, Science and Technology program within a unit on Food and Energy or as part of a geometry unit. It can also be used in the Grade 10 Community Ecology unit or in Grade 10 Geometry. It is best used after the activity "Can Our Planet Feed Us All?" Learning Outcomes Teaching, learning and evaluation will focus on the student's ability to: Make a moebius strip; Understand the concept of the "cycles of nature;" Appreciate that the producers of our food must work within the cycles of nature; Determine how changes within our own habits can enable us to live in harmony with nature's cycles. Classroom Development Provide students with the following: 3 cm widths of paper, cut from the long side of 28 cm x 43 cm sheets, enough for 2 per student; tape; pencil crayons;

68. Winding Clusters In Percolation On The Torus And The Moebius Strip Title Winding clusters in percolation on the Torus and the moebius strip The numerical results for the moebius strip and the number distribution of http://adsabs.harvard.edu/abs/2003cond.mat.10361P

Smithsonian/NASA ADS arXiv e-prints Abstract Service Find Similar Abstracts (with default settings below arXiv e-print (arXiv:cond-mat/0310361) References in the Article Also-Read Articles Translate Abstract Title: Winding clusters in percolation on the Torus and the Moebius strip Authors: Pruessner, Gunnar Moloney, Nicholas R. Journal: eprint arXiv:cond-mat/0310361 Publication Date: Origin: ARXIV Keywords: Statistical Mechanics Comment: 20 pages, 9 figures, submitted to J. Stat. Phys; J. Stat. Phys. 115, 839853 (2004) Bibliographic Code: 2003cond.mat.10361P Abstract Using a simulation technique introduced recently, we study winding clusters in percolation on the torus and the Moebius strip for different aspect ratios. The asynchronous parallelization of the simulation makes very large system and sample sizes possible. Our high accuracy results are fully consistent with predictions from conformal field theory. The numerical results for the Moebius strip and the number distribution of winding clusters on the torus await theoretical explanation. To our knowledge, this study is the first of its kind. Bibtex entry for this abstract Preferred format for this abstract (see Preferences) Find Similar Abstracts: Use: Authors Title Keywords (in text query field) Abstract Text Return: Query Results Return items starting with number Query Form Database: Astronomy/Planetary Instrumentation Physics/Geophysics arXiv e-prints Smithsonian/NASA ADS Homepage ADS Sitemap Query Form Preferences ... FAQ

69. © PSYCHOMEDIA - JOURNAL OF EUROPEAN PSYCHOANALYSIS - Judith Feher The New moebius strip Biology Starts in the Other. Judith FeherGurewich.Keywords Lacan Ð Neurosciences - Lesley Rogers - Biological Intersubjectivity http://www.psychomedia.it/jep/number14/gurewich-feher.htm

70. [Gilles Jobin] « The Moebius Strip » So The moebius strip, Gilles Jobin’s most recent creation, does not hold track When you ride a moebius strip, it is like going back to the beginning, http://www.parano.org/rubrique.php3?id_rubrique=78

71. Music moebius strip Tease. Nicolas Slonimsky was a theorist and composer who You can judge for yourself when you listen to his piece moebius strip Tease. http://www.math.ohio-state.edu/~fiedorow/math655/yale/music.htm

Music Click on the Chapter or Subchapter you wish to read. Preface for Teachers Introduction to Orientability: A Fable The Math of Non-Orientable Surfaces Surface and Manifold ... Bibliography Introduction The close connection which exists between music and mathematics takes on a new dimension, literally, when it comes to Moebius strips and music. If you are at all confused when going through our examples, just remember: a Moebius strip is a loop with a twist. If you take a piece of music, and it can be played through from the beginning to the end sounding harmonically and melodically correct (basically, sounding nice), you have gone around the Moebius strip once. Then, if you can go through it a second time, yet you start at the end of the piece, so that the last note of the piece becomes the first note of the piece, and it still sounds nice, you have Moebius music. Still confused? Take a look at the examples we found. Print them, cut them out, glue them into Moebius trips, and see for yourself! Bach and Schoenberg and Moebius Strips Johann Sebastian Bach wrote a lot of canons, and experimented with all sorts of different forms. The one which is most interesting for our purposes is from his “Musical Offering.” His canon for two violins, also called “crab canon,” is written so that you can play it normally, from one end to the other, and then you can take the score of music, flip it upside down, and play it again. Use the buttons below to listen to the music and look at the score at the same time. Keep in mind these

72. Moebius Strip moebius strip, what is it, see an avi movie. In other words one strip becomesa Möbius of order 1. What do you get if you cut the strips down the http://www.cut-the-knot.com/do_you_know/moebius2.shtml

Username: Password: Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Date: Tue, 21 Oct 1997 17:00:34 +0200 From: To: Alexander Bogomolny Hello Alexander Here is an interesting thing to do with 2 Möbius strips. Firstly, some background : Years ago I saw a problem posed by Martin Gardener. It went something like this : Take two strips of paper, glue them together without twisting them so that you have two cylinder like structures. Now glue the outsides together at a 90 degree angle. Now you cut the strips down the middle. The resulting shape will be a square. (That is if your stips are of equal length.) Now do the same again, but this time twist one strip. In other words one strip becomes a Möbius of "order" 1. What do you get if you cut the strips down the middle? The answer of course is another square. Now to the interesting part: Do the same as above but this time twist both strips. What do you get if you cut the strips down the middle? The answer is not obvious, it depends on the direction of the turns. if both strips are turned in the same direction then you will get a two separate pieces, one of which is completely twisted and the other is a "biangle", if I may call it that!

73. MOEBIUS STRIP What has been created is a flat moebius strip. Subject Easy moebius strip *Date Tue, 7 Jun 1994 135742 GMT +1200 51 * From Paul Batten http://www.is.kiruna.se/~cjo/d2i/MOEBIUS.STRIP.html

Contents page Index MOEBIUS STRIP Now extrude your line object along the moebius path. Use enough sections to get it as smooth as you desire. Also, set it so that the y is aligned to the path. Otherwise, it won't twist. What has been created is a flat moebius strip. If you want to have some thickness, you could extrude a 4point plane along the path(the y-axis for the plane should be perpendicular to the plane's surface). You may also want to add a 3rd point to the path by fracturing or splitting it. This will give you more control over the shape. If you add the 3rd point after doing the initial steps above, then you won't have to worry about rotating it on its local yaxis. * Subject: Easy Moebius Strip * Date: Tue, 7 Jun 1994 13:57:42 GMT +1200 [51] * From: "Paul Batten" <BATTENP@scico1.chchp.ac.nz> In the detail editor: 1. Add a closed path 2. Add a primitive plane, say 40x20 1 section 3. select the plane, choose Extrude: Along Path (the closed path in 1.), Align Y to Path, Sections = 100, Y Rotation = 180 ( to give the Moebius loop). Perform extrude. 4. You may need to edit the 8 faces where the 1st and last planes join, the seem to get twisted.

74. Articles, TOUT-FAIT: The Marcel Duchamp Studies Online Journal moebius strips (see Animation 1 which explains a possible genesis of the stripstarting from a As we saw before, moebius strip has a similar property. http://www.toutfait.com/issues/volume2/issue_5/articles/giunti/giunti3.html

Complexity Art by Roberto Giunti 3. Topology click still images to enlarge Figure 14 Figure 15 M. C. Escher Moebius band I M. C. Escher Moebius band II Animation 1 Animation of Moebius Strips Klee, Duchamp and Escher were all three attracted by topologically interesting figures. Several of Escher’s works deal with topological figures, such as knots ( Knots , 1965) and Moebius strips (as in Moebius band I (Fig. 14) and Moebius band II (Fig. 15) Moebius strips (see Animation 1 which explains a possible genesis of the strip starting from a cylinder) exhibit a number of interesting properties; I’ll recall and briefly explain some of them. First, unlike the cylinder, which has both an internal and external surface, the Moebius strip has only one surface; This can be easily verified by mentally painting its whole surface, without lifting the brush from the strip. Second, whilst a cylinder has two edges (lower and higher) the Moebius strip has one only edge; once again you can follow this edge completely with the finger without having to lift it from the edge.

75. Actionscript Forum - Moebius Strip Devils Playground Just something I wanted to shareYesterday there was a threadover at I put something together very. http://flash-forum.flashdevils.com/showthread_fd/t-346.Moebius strip.html

//top.location.href = "http://flash-forum.flashdevils.com/showthread.php?threadid=346"; document.title = "FlashDevils Community Archive, Flash Developer to Flash Developer - Moebius strip"; FlashDevils Community Archive Worth Checking Out Devils Playground Moebius strip - Click HERE for Original Thread XemonerdX Just something I wanted to share... Yesterday there was a thread over at We're Here about Moebius strips ... I put something together very quickly, just thought I'd also post it here :) http://www.poeticterror.com/exp/moebius.swf http://www.poeticterror.com/exp/moebius.zip (FlashMX fla) It doesn't have any z-sorting or filled faces or anything, but I hope you can see the Moebius-strip clearly enuf... BTW, a Moebius-strip is a surface that has only one side (a piece of paper has 2 sides for instance), which makes it a nonorientable surface. If you picture yourself walking on one side of the strip and you walk down the strip till you come back to your starting point, you will have walked on ALL parts of the strip, whereas if you do the same on a strip of paper, you will have walked on only 1 side and not on the other side. Interesting, no? :)

76. Moebius(1): Escher's Moebuis Strip II, With ... - Linux Man Page DESCRIPTION. Another MC Escher hack by Marcelo Vianna, this one draws ``MoebiusStrip II, a GL image of ants walking along the surface of a moebius strip. http://www.die.net/doc/linux/man/man1/moebius.1.html

moebius(1) - Linux man page NAME moebius - Escher's Moebuis Strip II, with ants. SYNOPSIS moebius [-display host:display.screen ] [-visual visual ] [-window] [-root] [-delay number ] [-solidmoebius] [-wireframe] [-noants] [-fps] DESCRIPTION Another M. C. Escher hack by Marcelo Vianna, this one draws ``Moebius Strip II,'' a GL image of ants walking along the surface of a moebius strip. OPTIONS -visual visual Specify which visual to use. Legal values are the name of a visual class, or the id number (decimal or hex) of a specific visual. -window Draw on a newly-created window. This is the default. -root Draw on the root window. -delay number Per-frame delay, in microseconds. Default: 20000 (0.02 seconds.). -solidmoebius Solid Floor. -wireframe Render in wireframe instead of solid. Draw Ants. Boolean. Whether to show a frames-per-second display at the bottom of the screen. ENVIRONMENT DISPLAY to get the default host and display number. XENVIRONMENT to get the name of a resource file that overrides the global resources stored in the RESOURCE_MANAGER property. SEE ALSO X xscreensaver AUTHOR Marcelo Vianna.

77. Xah: Surface Gallery moebius strip. Rotate View (Java Applet) The Mobius Strip Hermann Karcher ParametricEquations x = aa * (cos(v) + u * cos(v / 2) * cos(v)) y = aa * (sin(v) http://www.xahlee.org/surface/moebius_strip/moebius_strip.html

If you spend more than 30 minutes on this site, please send $1 to me. Go to http://paypal.com/ and make a payment to xah@xahlee.org. Or send to: P. O. Box 390595, Mountain View, CA 94042-0290, USA. ☠back to surface gallery Moebius Strip Rotate View (Java Applet) Supporting files: Rotater surface file a9.com search ☠back to surface gallery Xah Lee . Please send comments to xah@xahlee.org

78. SWISS FILMS The moebius strip. A sensual, fluid, hypnotic exploration of a “human sculpture”the bodies of five dancers pass, cross, follow, intertwine with each other http://www.swissfilms.ch/detail_f.asp?PNr=-2052785389

79. Hit And Run The Fargo moebius strip. When the Coen Brothers kicked off the fictional filmFargo with the announcement that This is a true story, little could they http://www.reason.com/hitandrun/2003/06/the_fargo_moebi.shtml

Continuous news, views, and abuse by the Reason staff Main Reason magazine Home About Subscribe Reason Online headlines (September 16) Jail, or Jail Not. There Is No Try.: Chief Justice Roberts will help decide whether an indefinite war requires indefinite detention (September 16) Stem Cell Therapies Next Year?: Korean researcher plans cloned stem cell transplants in 2006 (September 15) February 27, 2005 - March 05, 2005 February 20, 2005 - February 26, 2005 February 13, 2005 - February 19, 2005 Complete Archives Syndicate: xml or rdf June 09, 2003 The Fargo Moebius Strip When the Coen Brothers kicked off the fictional film Fargo with the announcement that "This is a true story," little could they have ever imagined that a Japanese girl would apparently hunt for the buried loot five years later, and end up dead in the snow. Or that a British journalist would retrace her steps with a Japanese actress, and discover that the life-imitates-weird-art story was truer (and therefore, falser) than anyone ever knew. Link via Scott MacMillan Posted by Matt Welch at June 9, 2003 01:59 AM

80. Hit And Run Discussion On The I Fargo /i Moebius Strip http//www.reason.com/mt31/mttb.cgi/1562. Listed below are links to weblogs thatreference The Fargo moebius strip from Hit and Run. http://www.reason.com/mt31/mt-tb.cgi?__mode=view&entry_id=1844

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