21. Moebius Strips In Knitting What is a moebius strip, and how do you use it in knitting? http://www.fuzzygalore.biz/articles/moebius.shtml

FUZZY GALORE knit patterns learn ... home Moebius strips in knitting A Moebius strip is the formal name of the mathematical object whose discovery is now attributed to the German mathematician Moebius . Apparently, this was really discovered by another mathematician called Listing , but he was only Czech so he doesn't get the credit :-). Without splitting hair about the mysteries of attribution, this is a fascinating object, which has only one side and one surface even though it looks to have more at first glance. The neat part is that since it's the simplest of its topological category we can easily make a physical model of it. The next step up, the Klein bottle, requires some imagination and can only be modeled in our pedestrian world with a large measure of cheating. There are a variety of geek explanations of how easy it is to convince yourself of a Moebius strip's properties, which I highly recommend you do. Moebius strips have intrigued artists before our time, for instance Escher who did this ant picture. Moebius strips were first popularized in knitting by Elizabeth Zimmerman , whose fertile and curious mind immediately seized on possible applications. She first came up with a free-standing Moebius strip as a scarf. There are many advantages to the Moebius approach to scarves, which make us personally fanatics about them. One is that it's practically impossible to lose a scarf that has no ends - you'd have to step over it to leave it behind, even if it had somehow managed to drop over your entire body. Another is that wear is completely even, since it gets worn subtly differently every time you pick it up, it's all the same so the actual position varies. You never get the thinned behind the neck part and splayed out ends that affect many knitted scarves after a short while.

22. The New York Times > Movies > THRU THE MOEBIUS STRIP > Review, Cast And Synopsis The NY Times review of Thru the moebius strip, a Glenn Chaika film starring and .Thru the moebius strip movie trailer, showtimes, tickets and reader http://movies2.nytimes.com/gst/movies/movie.html?v_id=296121

23. Graphics Archive - Flat Moebius Strip By Henry Rowley Flat moebius strip by Henry Rowley. CoArt.com. This moebius strip is isometricto a flat rectangle, which differs from the standard parametrization. http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Topology/moebius_strip.html

Graphics Archive Up Comments Special Topics ... Topology Flat Moebius Strip by Henry Rowley This moebius strip is isometric to a flat rectangle, which differs from the standard parametrization. The steps involved in its creation are found in Rowley's Summer Institute 1991 report. How to make it: Mathematica was used to obtain the parametrization, and MinneView (the precursor to Geomview) was used to view it. Image created: summer, 1991 The Geometry Center For permission to use this image, contact permission@geom.umn.edu External viewing: small (100x100 2k gif), medium (500x500 20k gif), or original size (400x400 15k tiff). The Geometry Center Home Page Comments to: webmaster@www.geom.uiuc.edu Created: Sat May 22 23:17:49 CDT 1999 - Last modified: Sat May 22 23:17:49 CDT 1999

24. The Moebius Strip The moebius strip Arnita Newton Kenwood Academy 4800 Chicago Beach Drive 5015 Instruct students to cut the moebius strip along the line they drew. http://www.iit.edu/~smile/ma9113.html

The Moebius Strip Arnita Newton Kenwood Academy 4800 Chicago Beach Drive 5015 Blackstone Avenue Chicago IL 60615 Chicago IL 60615 312-548-1446 312-535-1350 Objective : To investigate mathematical patterns using the Moebius Strip. Materials Needed : Strips of paper 10 inches long and 2 inches wide. Adding machine tape, construction paper or graph paper. Allow 10 strips for each student. Markers or colored pencils optional. Students will also need Scotch "Magic" tape and scissors. Strategy : Students are asked to examine their strips of paper to determine that each strip Conclusion : The Moebius Strip is an interesting topological figure. The investigation also provides a good exercise in having students derive a generalization from their empirical observations. Return to Mathematics Index

25. Moebius Strip@Everything2.com moebius strip. See Mobius strip successfully after being fed the remains ofa successful worm Moebius Why did the chicken cross the Mobius strip? http://www.everything2.com/index.pl?node_id=22410

26. Boing Boing: Moebius Double twist strip playground equipment Real moebius strips have anodd number of twists, and thus have only one side. http://www.boingboing.net/2004/07/28/moebius_double_twist.html

Moebius Double twist strip playground equipment @import url(http://www.boingboing.net/table.css); suggest a site rss archives store ... john Sponsored by: HOWTO: Get a link posted to Boing Boing Boing Boing Mobile powered by Winksite Fark rules! Our Linking Policy This work is licensed under a Creative Commons License Stats (About our stats) Our first five years' worth of posts in one file Wednesday, July 28, 2004 Moebius Double twist strip playground equipment Kevin Jarnot sez: "Little Tikes Commercial has created a playground structure called the "Infinity Climber", which is a climbable Moebius double twist strip for kids. It also recently won a 2004 Industrial Design Excellence Award (IDEA)" Link Cassidy Curtis sez: "I hate to break it to your readers, but that piece of playground equipment is not really a Moebius strip. It has two twists, not one, which means it's an orientable surface (having two unique sides), topologically equivalent to an ordinary circular strip. A kid on one side of the strip could crawl around forever and not meet any kids on the other side. Real Moebius strips have an odd number of twists, and thus have only one side." Kevin McCarty sez:That's not quite right either. A two-twist strip is not topologically equivalent to a no-twist strip, nor to a one-twist strip (the Moebius strip). They're all topologically inequivalent. The two circular edges of the 2-twist strip are linked, while with the 0-twist strip they're not. For all integers n, the n-twist strips are inequivalent to each other. The ones with even number of twists are orientable with two circular edges with varying linking number, and the odd-numbered twists are non-orientable with a single circular edge that links (knots) itself a varying number of times. Welcome to the wonderful world of homotopy equivalence classes.

27. Boing Boing: What Is Palladium? What Is The Area Of A Moebius Strip? What is the area of a moebius strip? Many nice things in Seth s journal today,especially. I ve been having a debate with a friend about how to calculate http://www.boingboing.net/2002/07/04/what_is_palladium_wh.html

@import url(http://www.boingboing.net/table.css); suggest a site rss archives store ... john Sponsored by: HOWTO: Get a link posted to Boing Boing Boing Boing Mobile powered by Winksite Fark rules! Our Linking Policy This work is licensed under a Creative Commons License Stats (About our stats) Our first five years' worth of posts in one file Thursday, July 4, 2002 What is Palladium? What is the area of a Moebius Strip? Many nice things in Seth's journal today, especially: I've been having a debate with a friend about how to calculate the area of a moebius strip, where the moebius strip is constructed by taking a 1" by 10" area, twisting it, and joining the ends... My observation was that if you did make the strip from paper, you would need 20 sq. in. of paint in order to paint the whole thing. If you used 10 sq. in. of paint, you would have 10 sq. in. of surface unpainted. However, Jonathan argues that this is a misinterpretation if the Möbius strip is seen as having zero thickness, because then points on one "side" are actually identical with the corresponding points on the "other side". He suggests that, on a zero-thickness strip, you can go only 10" before you return to your starting point. (On a strip made of paper with non-zero thickness, you must go 20" before returning to your starting point.) And don't miss: Five people came from Microsoft to meet with us on Tuesday about Palladium. It was very interesting.

28. MSN - Movies Thru The Moebius Strip MSN MOVIES, 4, Thru the moebius strip. Rate this movie. More About this Movie.Main Page. User Reviews Thru the moebius strip. Science Fiction. 2005 http://movies.msn.com/movies/movie.aspx?m=556068

29. Moebius Strip A moebius strip is a onesided surface that can be constructed by affixing theends of a rectangular strip after first having given one of the ends a http://abyss.uoregon.edu/~js/glossary/moebius_strip.html

Moebius strip A moebius strip is a one-sided surface that can be constructed by affixing the ends of a rectangular strip after first having given one of the ends a one-half twist. This space exhibits interesting properties, such as having only one side and remaining in one piece when split down the middle. The properties of the strip were discovered independently and almost simultaneously by two German mathematicians, August Ferdinand Moebius and Johann Benedict Listing, in 1858. Excerpt from the Encyclopedia Britannica without permission.

30. Funology.com -- Abracadabra --Moebius Strip Funology.com the science of having fun! Funology.com is the premiere onlinedestination for kids. We offer tons of fun, creative activities, games, http://www.funology.com/abracadabra/abra010.htm

Your Ad Here Moebius Strip What You'll Need Paper Tape Marker You can amaze your friends with this piece of paper that has only one side! Here's how to do it: Cut a long, skinny strip of paper. Make a loop with the paper by matching up the narrow ends. Make one twist into the paper and tape the ends together. With your marker, start drawing a line on the piece of tape and continue the line without lifting your marker until you meet up at the tape where you started. You drew a line on both sides of the strip of paper without lifting your marker. The paper only has one side! Home Link to Us Legal Sponsor Information ... Contact Us

31. Escher: Moebius Strip II (Red Ants) moebius strip II (Red Ants) 1963 Woodcut printed from three blocks 45.3 x 20.5cm (17 7/8 x 8 1/8 in.) © Cordon ArtBaarn-the Netherlands. http://www.artchive.com/artchive/E/escher/escher_red_ants.jpg.html

32. Moebius Movie Review In this way, the moebius strip explores the nature of infinity on many differentlevels. I think the film could ve incorporated more information about the http://www.ram.org/ramblings/movies/moebius.html

33. Snow Moebius Strip: Doing The Twist - The Daily Californian created the team’s design based on a triply twisted moebius strip. Such amoebius strip is constructed by joining the two ends of a rectangular piece of http://www.dailycal.org/article.php?id=18041

34. Thru The Moebius Strip Thru the moebius strip showtimes, review, ratings, synopsis, plot summary,trailer, premiere, interviews, photos, cast and crew, locations, distributors, http://www.hollywood.com/movies/detail/movie/1741267

MPShowAd("2x2", "", "", "MOAC", "", "Animated", "Fantasy", "Sci-Fi", "", "", "", "", "t1", "", "listed","1741267"); MPShowAd("2x2", "", "", "MOAC", "", "Animated", "Fantasy", "Sci-Fi", "", "", "", "", "t1", "", "listed","1741267"); MPShowAd("728x90", "", "", "MOAC", "", "Animated", "Fantasy", "Sci-Fi", "", "", "", "", "t1", "", "random","1741267"); Hollywood.com The Web MOVIES DVD CELEBS VIDEO ... login MPShowAd("503x50,503x100", "", "", "MOAC", "", "Animated", "Fantasy", "Sci-Fi", "", "", "", "", "t1", "", "random","1741267"); Movie Info Trailer Reviews Interviews Premiere Official Site Thru the Moebius Strip this film is not currently playing in theaters Animated, Fantasy, Sci-Fi RATE IT! Average User Rating: About Thru the Moebius Strip A boy travels to a magical, alien world of giants to find his long-lost father and realize his own destiny. ... more This ad pays the bills, but we live for what comes after it. Keep reading! MPShowAd("300x250", "", "", "MOAC", "", "Animated", "Fantasy", "Sci-Fi", "", "", "", "", "t1", "", "random","1741267"); THE PLOT...

35. Thru The Moebius Strip Film Movie Trailer Review At The Z Review XXXX coming soon film movie and trailer review at The Z Review the best UK comingsoon trailer and movie review site for information on XXXXX. http://www.thezreview.co.uk/comingsoon/t/thruthemoebiusstrip.shtm

Home News Coming Soon Movie Trailers ... Contact Thru The Moebius Strip Thru The Moebius Strip Expected Release Date U.S. : Expected Release Date U.K. : (subject to change) Expected Rental Release Date : (subject to change) Thru The Moebius Strip Cast : Mark Hamill, Chris Marguette, Michael Dorn, Kellie Martin, Jonathan Taylor Thomas and Jean Simmons Director : Glenn Chaika Thru The Moebius Strip Written By : Jim Cox and Paul Gertz Producers : Other Known Crew Members Thru The Moebius Strip Based On :A story idea by Jean "Moebius" Giraud Premise/Synopsis : Story of physicist Simon Weir, who becomes lost and trapped in a space-time portal he created. His son must search for him through a myriad number of planets, filled with wondrous sights and often gigantic beings. Genre : Sci Fi/Comic Book Thru The Moebius Strip Official Site : Fan Sites : Thru The Moebius Strip Trailer : Released By :

36. Nexus - How Come?: Moebius Strip On How Come, we discover the surprising properties of the moebius strip. A loopof paper with only one side and one edge, the moebius strip can be cut in http://abcasiapacific.com/nexus/stories/s839189.htm

Home About ABC Asia Pacific ABC Shop Contact Us ... How Come? Moebius Strip Tuesday, 29 April 2003 On How Come, we discover the surprising properties of the Moebius Strip. A loop of paper with only one side and one edge, the Moebius strip can be cut in half or in thirds - but it doesn't always give you the result you might expect. We try to find out how it works and why and look at more surprising mathematics, all explained by the science of topology. Previously in How Come?... top of page Links: Moebius Strip - Questacon The Moebius Strip The Möbius Strip [an error occurred while processing this directive]

37. Chess In A Moebius Strip Chess in a moebius strip. Take the Cylindrical 8 x 14 Variant. Klein Chess,if the moebius strip is glued again, along the a and h columns. http://www.chessvariants.org/shape.dir/x_moeb.html

Contact Form What do you want to do? Get Technical Support Ask a Question Submit Content Report a Bug Send in a Correction Find Opponents for a Game Share our opinions Help us with this website Contact a Specific Editor Send us mail (not email) Something else More Information on this item Kriegspiel is September's Recognized Chess Variant of the month. Rate this page! Skip to comments Chess in a Moebius Strip Take the Cylindrical 8 x 14 Variant . Why should the board be glued so nicely? Why not twist it before the glue? The board would still look like the picture below, however, along the 11th/12th (or -3rd/-2nd) junction, there would be a "inversion", so that a11 would join h12, b11 would join g12, and so on: All other rules (castling, en-passant, promotion, etc) apply. An interesting aspect of this board is that, while on most standard variants, the King is facing the other King, here, along the 8-9-10-11-12-13-14-15 board, each King is facing the opponent's Queen. The Moebius Strip is a non-oriented surface. While this concept can hardly apply to chess, a minor consequence is that the Bishops don't have a fixed colour: a bishop that starts in a "White" square (say, f1) can chance to a "Black" square (f1-a6-b12). A sample game could be: 1- d12 e11 [actually in front of the d12 pawn] 2- c12 [White is playing a Queen's Gambit, while Black is playing a King's Gambit!] 2- ... exc12 3- e12 g11 [defending the c12 pawn]

38. Double Moebius Strip Studies By Petresin And Robert In The Nexus Vesna Petresin and LaurentPaul Robert show that the Möbius strip has a greatpotential as an architectural form, but we can also use its dynamics to reveal http://www.nexusjournal.com/PetRob.html

39. The Mobius Strip For another perspective, view a moebius strip presentation movie, click tohttp//www.drasticcreations.com/projects/mobius/ http://www.mobiusproductsandservices.com/tms.html

The Mobius Strip was discovered in 1858 by German mathematician and astronomer August Ferdinand Mobius (1790-1868). The mathematical equation is known as The Mobius Transformation, also known as bilinear transformation or linear fractional transformation. (Webster's dictionary:" A map of the complex plane to itself in which a point "z" is mapped to a point "w" by w=(az+b)/(cz+d), where a,b,c, and d are complex numbers and ad-bc does not equal zero.") It is a continuous loop with one surface and one edge formed by twisting one end of a long, thin rectangular strip 180 degrees (1/2 twist) and attaching this end to the other. This fascinating shape expresses Transformation. Today the Mobius Strip has been chosen as the Universal symbol of recycling. It represents the process of transforming waste materials into useful resources. On a personal level, the Mobius strip represents a willingness to move WITH the constantly changing cycles in our Life process, transforming our challenges into useful solutions. The Mobius Strip reveals planetary transformation,as well. Historically, there has always been Earth changes,i.e. natural re-structuring of land and ocean masses, tide changes, weather changes, seasonal changes, etc. The Mobius Strip shape is symbolic of eternal change within stillness itself.

40. 01/29/2004: " 01/29/2004 Archives Thru the moebius strip film in postproduction, As wepreviously reported, Thru the moebius strip is about physicist Simon Weir, http://www.animated-news.com/archives/00000771.html

film in post-production, to become TV series" Home Archives Forum Mailing List ... to debut at Cannes" 01/29/2004 Archives: " Thru the Moebius Strip film in post-production, to become TV series" ComingSoon.net reports on a Variety story about Jean Giraud's sci-fi fantasy film Thru the Moebius Strip . Senator International will handle worldwide sales rights of this CG feature written by Jim Cox and Paul Gertz. Currently in post-production, Moebius will be completed this year. The film features the voice talents of Mark Hamill, Chris Marguette, Michael Dorn, Kellie Martin, Jonathan Taylor Thomas, and Jean Simmons. As we previously reported Thru the Moebius Strip is about "physicist Simon Weir, who becomes lost and trapped in a space-time portal he created. Eight years later, his son, Jac Weir, must search for him through a myriad number of planets, filled with wondrous sights and often gigantic beings". AWN adds that the film, budgeted at just $8 million, was recently screened in Las Vegas at the NAPTE (National Association Of Television Program Executives) Conference and Exhibition, is 74 minutes long, and is also being developed as a TV series. Posted by James at 8:18 am ET Contact Info

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