21. What Is The Mobius Strip? Ask the experts your physics and astronomy questions, read answer archive, and more. http://www.physlink.com/Education/AskExperts/ae401.cfm

xUmp.com Science Toys Ask the Experts University Departments ... Amazon.com Widgets Need an interior designer in the Los Angeles area? Visit: Odeau.com Question What is the Mobius Strip? Asked by: Kartikeya Shah Answer Very roughly a surface is orientable if it has two sides so that, for example, is it possible to paint it with two different colours. A sheet of paper or the surface of a sphere are examples of orientable surfaces. A Mobius strip is a non-orientable surface: you can build one with a strip of paper (twist the strip and glue end together to form a ring) and verify that it has only one side: it is not possible to paint it with two colours. In short a Mobius strip only has one side and one edge. Ants would be able to walk on the Mobius strip on a single surface indefinitely since there is no edge in the direction of their movement. Just like what M.C. Escher depicted in his famous picture (shown on the right.) Mobius strip was named after the astronomer and mathematician August Ferdinand Möbius (1790-1868). He came up with his 'strip' in September 1858. Independently, German mathematician Johann Benedict Listing (1808-1882) devised the same object in July 1858. Perhaps we should be talking about the Listing strip instead of the Mobius strip. To learn more about the Mobius strip go to: ScienceNews MathTrek Learn more about the Mobius strip at Fermilab You can buy Escher's 'Ants' poster by clicking here Answered by: Dan Summons, Theory Physics Undergrad Student, UOS, Souhampton

22. Möbius Strip A M bius strip is a ribbon of material that has only one side. A group of nanotechnology researchers experimenting with manipulating tiny objects was able to reshape a DNA strand http://www.neatorama.com/tag/mobius-strip/

@import url(http://static.neatorama.com/img9/style-reg.css?version=1); Quick Login Regular Login Register Neat Stuff ... Small Gifts RSS LITE TOPICS Business Collaborations ... Scientists Fold DNA into Möbius Strips Posted by John Farrier in on October 4, 2010 at 5:31 pm A Möbius strip is a ribbon of material that has only one side. A group of nanotechnology researchers experimenting with manipulating tiny objects was able to reshape a DNA strand into a Möbius strip. The ability to create complex structures on the tiniest of scales is one of the great challenges of nanotechnology. In particular, chemists are looking for particular topological structures, or structures that keep their basic properties no matter how much you stretch or twist them. A Möbius strip is a good example of such a structure, because no matter what you do it (short of tearing it, of course), it will always have only one side. Link Journal Article et al neatorama445:http://www.neatorama.com/2010/10/04/scientists-fold-dna-into-mobius-strips/ Möbius Comic Strip Posted by John Farrier in on September 21, 2010 at 9:02 am

23. Möbius Strip - Simple English Wikipedia, The Free Encyclopedia The M bius strip or M bius band is a surface with only one side and only one edge. It can be made using a strip of paper by gluing the two ends together with a halftwist. http://simple.wikipedia.org/wiki/Möbius_strip

Möbius strip From Wikipedia, the free encyclopedia Jump to: navigation search A Möbius strip A wedding ring designed as a Möbius strip. The Möbius strip or Möbius band is a surface with only one side and only one edge. It can be made using a strip of paper by gluing the two ends together with a half-twist. The twisting is possible in two directions; so there are two different (mirror-image) Möbius strips. The Mobius strip is known for its unusual properties. A bug crawling along the center line of the loop would go around twice before coming back to its starting point. Cutting along the center line of the loop creates one longer band, not two. Cutting one third of the way in from the edge (and parallel to it) produces another amusing result. The Möbius strip was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858. Contents Mathematical description Möbius bands in nature and technology Other pages References ... change Mathematical description A parametric plot of a Möbius strip To turn a rectangle into a Möbius strip, join the edges labelled

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thefind.onloads.add("tr_size('f2e3c00b35b298d62c8352002578ebcd%3A0000');"); Sign in Create account Shop The Web Shop Nearby Shop Like Me Shop Like Friends Sneak Peek! Prices Prices range from to Min Max to update Sales Coupons Shipping Deals Stores Choose Stores Local Stores Sort by: Best Results Alphabetical Better World Books geocoinstore Amazon.com Buy.com Etsy Borders monkeysarcades Knitting Today PAPAMEDIA.COM Amazon Marketplace fibertrends doverpublications 5 Star Shine Earth Faire heartstringsfiberarts daaveedee Miss Malaprop waldorf-books Vedic Books Buy.com Marketplace Columbine Yarns patternfish CVMC bobandnancysbookshoporg bobandnancysbookshop and other marketplaces Colors Pick Colors Filter by color: Adjust your color: Use this color: Brands Select Brands Sort by: Best Results Alphabetical Fiber Trends Forme Pawprints Mobius Infinity Dover Publications As You Wish Easy Checkout Certified Secure Top Searches balenciaga bag converse sneakers tank dress evening gowns ... draped dress Popular Searches simplicity bassinet ibook clamshell ocean art ed hardy cap ... Reviews Found 25 stores with 37 products matching moebius strip Web Results Sort by: Lowest Price Highest Price Best Results Share: Quick Look Fiber Trends - AC39e Lace Moebius Scarf -PDF Fiber Trends Pattern AC39e - PDF Design by Sarah Hauschka A Moebius strip has only one surface, and only one edge. Intriguing to knit, this geometric oddity makes a beautiful yet functional scarf. When placed around the neck, it crosses itself in front and stays in place. If looped again around the neck, it becomes a snug neck scarf and if you pull one edge up over your head it becomes a wimple, as shown at top in photo. Size: Approximately 52" (132cm) in circumference and 16" (40cm) wide. Yarn

25. Möbius Strip On Myspace Music - Free Streaming MP3s, Pictures & Music Downloads MySpace Music profile for M bius Strip. Download M bius Strip Indie / / music singles, watch music videos, listen to free streaming mp3s, read M bius Strip's blog. http://www.myspace.com/mobiusstripmusic

26. A 3D Mobius Strip, Latched Left, Modeling A Wave-Particle Quanton -- A Quantum O M bius Strip Latched Left Using Macsyma by Doug Renselle Using parametric equations provided by Paul Bourke x = cos(s) - t*cos(s/2) + cos(s) (-t left) http://www.quantonics.com/Level_4_QTO_Mobius_Strip_Quanton_Latched_Left.html

Arches Art If you're stuck in a browser frame - click here to view this same page in Quantonics! Using Macsyma - by Doug Renselle Using parametric equations provided by Paul Bourke x = cos(s) - t*cos(s/2) + cos(s) (-t left) y = sin(s) + t*cos(s/2) + sin(s) z = t*sin(s/2) Here's a MAC OS X Grapher example which only took a few minutes to do Doug took above parametric equations and made a new graphic using MAC OS X's 10.4 version of Grapher.app (a MAC 'utility') to do above art. Here are modified parametrics for Grapher which you can retype into a 3D 'New' Grapher file: Cut and paste piecemeal cosv - tcosv + cosv sinv + tcosv + sinv tsinv t=0...0.25 p , v=0...2 p Grapher animates above in a single plane of rotation. Too, you can control rotation rate. And you can grab its cubic frame and move and hold it to any position. Have some fun playing with omniffering plus and minus signs and p multipliers. If you like this work, you will love Grapher! It blows other graphic tools to smithereens. Doug - 11May2007.

27. Moebius-Strip - Anime Paper - Anime And Manga Wallpapers And Scans! (アニメ) An anime and manga community website for wallpapers and scans as well as a popular forum. http://moebius-strip.animepaper.net/

@import url("http://static1.animepaper.net/upload/css/696.css"); @import url("http://static3.animepaper.net/css/constant.css"); @import url("http://static1.animepaper.net/css/ui.css"); @import url("http://static1.animepaper.net/css/userpage.css"); login register Home Classic Home ... Moebius-Strip Welcome My Minitokyo page Moebius-Strip Lazy Donating Member Mr. Nobody Wallpapers Wallpaper Comments Scans User Comments ... Forum Posts Male 30 years old Last Online: Invisible Registered: March 21st, 2006, 9:24 PM EST Papers: 19730 Donated: Recent Scan Rena Special "Title Page" by $ Moebius-Strip 3 years 7 months ago Recent Scan Rena Special .hack//pinup by $ Moebius-Strip 3 years 7 months ago Banime Ningen Shinndou Pixelated Graffiti ... Advertisement Opportunities

28. M Bius Strip - Hutchinson Encyclopedia Article About M Bius Strip Structure made by giving a half twist to a flat strip of paper and joining the ends together. It has certain remarkable properties, arising from the fact that it has only one edge http://encyclopedia.farlex.com/Möbius strip

29. Möbius Strip: Definition From Answers.com n. A continuous onesided surface that can be formed from a rectangular strip by rotating one end 180 and attaching it to the other end. After August Ferdinand M bius http://www.answers.com/topic/m-bius-strip

30. Moebius Strip Earrings Make these earrings with size 11/0 cylinder beads in the shape of a Moebius strip, which has only one edge and one side. First, work a 4bead wide st http://www.instructables.com/id/Geek-chic-Moebius-strip-earrings/

31. Picture Gallery Moebius Strip I 1961 wood engraving and woodcut in red, green, gold and black Moebius Strip II 1963 woodcut in red, black and greygreen, printed from 3 http://www.mcescher.com/Gallery/gallery-recogn.htm

Picture gallery "Recognition and Success 1955 - 1972" Convex and Concave 1955 Lithograph Liberation 1955 Lithograph Rind 1955 wood engraving and woodcut in black, brown, blue-grey and grey, printed from 4 blocks Depth 1955 wood engraving in brown-red, grey-green and dark brown, printed from 3 blocks Three Worlds 1955 Lithograph Swans 1956 wood engraving Bond of Union 1956 Lithograph Print Gallery 1956 Lithograph Division 1956 woodcut, second state Smaller and Smaller 1956 wood engraving and woodcut in black and brown, printed from 4 blocks Plane Filling II 1957 Lithograph Whirlpools 1957 wood engraving and woodcut, second state, in red, grey and black, printed from 2 blocks Belvedere 1958 Lithograph Sphere Surface with Fish 1958 woodcut in grey, gold and reddish-brown, printed from 3 blocks Spher Spirals 1958 woodcut in grey, black, yellow and pink, printed from 4 blocks Flatworms 1959 Lithograph Circle Limit II 1959 woodcut in red and black, printed from 2 blocks Circle Limit III 1959 woodcut, second state, in yellow, green, blue, brown and black, printed from 5 blocks Ascending and Descending 1960 Lithograph Circle Limit IV 1960 woodcut in black and ocre, printed from 2 blocks

32. Möbius Strip A M bius Strip is a twisted loop, normally made of paper. Mathematical Idea. A twisted loop is very different from a normal loop. Materials Needed http://mathssquad.questacon.edu.au/mobius_strip.html

Questacon Questacon Canberra National Initiatives On Tour: Programs ... On Tour: Programs Möbius Strip Maths Squad Activities What is Topology? The Handcuffs Puzzle Handcuff Puzzle Images Möbius Strip ... Bubble Mix Recipe Mathematical Idea A twisted loop is very different from a normal loop. Materials Needed Strips of paper, sticky tape, scissors and a pen. Demonstration Strange Properties This long strip has four half-twists in it. If you cut it down the middle, you get two strips wound around each other. There are other combinations of strips that give interesting results when you cut down the middle of them: Double Twist Triple Twist Make a strip with three half-twists. This strip will have only one side and one edge. When you cut down the middle, the strip will become a knotted loop. Three variations on the double loop. You can also stick two strips together to get some interesting effects. (See illustration) Take two ordinary, untwisted loops. Stick them together at right angles to each other. With each set of strips, if you cut down the middle of both strips, you will get a square. How did two different shapes both end up making a square?

33. Science Fair Projects - Möbius Strip The Ultimate Science Fair Projects Encyclopedia M bius strip http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Mobi

All Science Fair Projects Science Fair Project Encyclopedia for Schools! Search Browse Forum Coach ... Dictionary Science Fair Project Encyclopedia For information on any area of science that interests you, enter a keyword (eg. scientific method, molecule, cloud, carbohydrate etc.). Or else, you can start by choosing any of the categories below. Science Fair Project Encyclopedia Contents Page Categories Surfaces Articles with ASCII art Möbius strip (Redirected from Mobius band The Möbius strip or Möbius band is a topological object with only one side (one-sided surface ) and only one boundary component . It was co-discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in . A model can easily be created by taking a paper strip and giving it a half-twist, and then merging the ends of the strip together to form a single strip. In Euclidean space there are in fact two types of Möbius strip depending on the direction of the half-twist: if the right hand twists the right end of the strip in a clockwise manner, the result is a

34. Fantagraphics Books - Moebius Strip Comic By Jim Woodring (video, Photo, Animati Sep 17, 2010 Photo courtesy the artist Moebius strip comic Jim Woodring. Looped animation Moebius strip comic - Jim Woodring http://www.fantagraphics.com/index.php?option=com_content&task=view&id=4

35. Möbius Strip: Facts, Discussion Forum, And Encyclopedia Article The M bius strip or M bius band (pronounced or in English, in German) (alternatively written Mobius or Moebius in English) is a surface http://www.absoluteastronomy.com/topics/Möbius_strip

Home Discussion Topics Dictionary ... Login Möbius strip Möbius strip Topic Home Discussion Discussion Ask a question about ' Möbius strip Start a new discussion about ' Möbius strip Answer questions from other users Full Discussion Forum Encyclopedia The Möbius strip or Möbius band (pronounced or in English, in German) (alternatively written Mobius or Moebius in English) is a surface Surface In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable Orientability In mathematics, orientability is a property of surfaces in Euclidean space measuring whether or not it is possible to make a consistent choice of surface normal vector at every point. A choice of surface normal allows one to use the right-hand rule to define a "clockwise" direction of loops in the... . It can be realized as a ruled surface Ruled surface In geometry, a surface S is ruled if through every point of S there is a straight line that lies on S. The most familiar examples are the plane and the curved surface of a cylinder or cone...

36. Howtoons » The Magical Moebius Strip The Magical Moebius Strip. click toon to enlarge Prev toon Next magic. Materials newspapers, tape. Category Play. Download .pdf to print http://www.howtoons.com/?page_id=187

37. Möbius Strip | Ask.com Encyclopedia A M bius strip made with a piece of paper and tape. If an ant were to crawl along the length of this strip, it would return to its starting point having traversed every part of the http://www.ask.com/wiki/Möbius_strip?qsrc=3044

38. Moebius Strips In Knitting Jan 25, 2005 What is a Moebius strip, and how do you use it in knitting? A Moebius strip is the formal name of the mathematical object whose 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.

39. YouTube - Moebius Strip II 1963 Escher Jan 22, 2010 Moebius Strip II 1963 Escher. Added to queue Escher Geomag Moebius strip by aldoaldoz25824 views 201. Add to http://www.youtube.com/watch?v=ZN4TxmWK0bE

40. Möbius Strip This page has been visited 32,992 times since 4 September 2007. Hits today 30 http://web.meson.org/topology/mobius.php

This page has been visited times since 4 September 2007. Hits today: 3 Home Languages Mathematics 4D Rotation Applet ... Contact Me Last modified: 18-Jan-2006 Atom feed for this site Let's start with something simple. Just about every kid learns about these early on. You take a strip of paper and join the ends in a loop after giving one end a half-twist so it joins up with the other one upside-down. If you've never tried this before, you should immediately (a) feel ashamed, and (b) try it out. The big deal about this is that it has only one side and one edge. The cool trick is that if you cut it in half lengthwise, it doesn't fall into two pieces. Instead, it makes one loop with two Seamless Topology A page on the web mentioned knitting one from the edge . Obviously it's simple enough to knit one: you can knit a strip and graft the edges together. But knitting it from the edge is another matter: You wind up with a strip with no seam! It also rather freaked me out when I realized it was working. I didn't actually understand the description used in the web page, so I did my best to interpret it and basically worked it out myself. The result is pretty cool. Here's what I did: start with a nice big circular needle (29-inch or so). I used one size 9, but it shouldn't matter much. Cast on a mess of stitches, at least enough to cover half the needle. Better to make it close to the whole thing

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