1. Moebius A moebius strip is a loop of paper with a half twist in it. How to make a moebiusstrip. What to do with a moebius strip. http://mathforum.org/sum95/math_and/moebius/moebius.html

The Moebius Strip A moebius strip is a loop of paper with a half twist in it. How to make a moebius strip. What to do with a moebius strip. Find it on the Web or at the Library. How to make a moebius strip. 1. Take a strip of paper. 2. Give it a half twist (turn one end over). 3. Tape the ends together. What to do with a moebius strip. After you make your moebius strip, take a pencil and draw a line along the length. How many sides does the moebius strip have? Take a pair of scissors and cut the moebius strip along the line you have drawn. What happened? What do you think will happen if you cut it down the middle again? Try it. Find it on the Web... Moebius was a mathematician and astronomer in the 1800s.  Take a look at the path of the ants on Moebius Strip II , a woodcut by M.C. Escher . Which side of the strip are the ants walking on? or at the Library. If you have trouble accessing the Escher graphics over the Web, check with your school or public library for a book of Escher's work, which includes a lot of interesting mathematical figures. Return to main Mathematics and...

2. Mobius Strip The M bius Strip 1. Start with a long rectangle (ABCD) made of paper. 2. Give the rectangle a half twist. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. Math Forum: Mathematics And... - Jan Garner Things to make. The moebius strip Polyhedra. Spreadsheets. Introduction to Mathand Spreadsheets Spreadsheet Basics and Graphing Examples http://mathforum.org/sum95/math_and/

Mathematics and... by Jan Garner Back to sum95 Projects Page Forum Web Units Art Perspective Drawing Things to make The Moebius Strip Polyhedra Spreadsheets Introduction to Math and Spreadsheets Spreadsheet Basics and Graphing Examples Download notes or examples. Visit SUNY Potsdam Home The Math Library Quick Reference ... Help http://mathforum.org/ The Math Forum comments to the Teacher Exchange 28 May 1996

4. Math Forum Mathematics And - Jan Garner Things to make. The moebius strip. Polyhedra http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. Moebius Strip Möbius strip, what is it, see an avi movie. It s possible to glue togethertwo bands of paper, be these cylinders or moebius strips. http://www.cut-the-knot.org/do_you_know/moebius.shtml

Username: Password: Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Sphere has two sides . A bug may be trapped inside a spherical shape or crawl freely on its visible surface. A thin sheet of paper lying on a desk also have two sides. Pages in a book are usually numbered two per a sheet of paper. The first one-sided surface was discovered by J. B. Listing .) The strip was immortalized by M. C. Escher strip of paper Twist one end 180 o (half turn) and glue the ends together (the avi file takes 267264 bytes). For comparison, if you glue the ends without twisting the result would look like a cylinder or a ring depending on the width of the strip. Try cutting the strip along the middle line. People unacquainted with Topology seldom guess correctly what would be the result. It's also interesting cutting the strip 1/3 of the way to one edge. Try it. I have put together a short (155648 bytes) avi movie Now once you know the trick, surely you would like to find other one-sided surfaces. Before gluing the ends together you can twist the strip twice or even three times. Do you get one-sided or two-sided surface? Acknowledgment: Without Mathcad the page would be a complete dud.

6. The Moebius Strip The moebius strip Arnita Newton Kenwood Academy 4800 Chicago Beach Drive 5015 Blackstone Avenue Chicago IL 60615 Chicago IL 60615 312548-1446 312- http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. Paper Strip What can be done with a paper strip plane annulus, moebius strip, torus, KleinBottle, Projective Plane. http://www.cut-the-knot.org/do_you_know/paper_strip.shtml

Username: Password: Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Paper Strip Activities We already had an example of how to transform a paper strip into the Moebius Strip. Here I want to expand on this kind of activity. In short, I plan to describe several surfaces obtained by gluing together sides of a paper strip in various fashions. Note that unless you do something drastic to the strip, the strip is topologically equivalent to a square which means there exists a continuous mapping from one to another. Amazing results are also obtained by toying with two pieces of paper simultaneously. First of all let's sum up the results in a table Diagram Properties Sidedness Avi movie file size Cylinder (plane annulus) Two boundary curves Two-sided Moebius Strip One boundary curve One-sided 267264 bytes Torus Closed surface Two-sided 389120 bytes Klein Bottle Closed surface One-sided 389140 bytes Projective Plane Closed surface One-sided A few words of explanation are in order. Given a square, we intend to associate (by gluing, if possible) points of its opposite sides. When arrows on the opposite sides point in the same direction as, for example, is the case of the annulus, we identify (glue together) points without twisting the sides. When arrows point in opposite directions one of the sides must be twisted a half turn (180 o ) before the points are identified. Such is the case of the

8. Graphics Archive - Flat Moebius Strip By Henry Rowley Flat moebius strip by Henry Rowley. This moebius strip is isometric to a flat rectangle, which differs from the standard parametrization. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. Möbius Strip -- From MathWorld Escher, MC moebius strip I. Wood engraving and woodcut in red, green, gold andblack, Classic Surfaces from Differential Geometry moebius strip. http://mathworld.wolfram.com/MoebiusStrip.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Topology Topological Structures Geometry ... cylinder , it is not a true surface, but rather a surface with boundary (Henle 1994, p. 110). Euler characteristic (Dodson and Parker 1997, p. 125). According to Madachy (1979), the B. F. Goodrich Company patented a conveyor belt in the form of a Möbius strip which lasts twice as long as conventional belts. M. C. Escher was fond of portraying Möbius strips, and they appear in his woodcuts "Möbius Strip I" and "Möbius Strip II (Red Ants)" (Bool et al. 1982, p. 324; Forty 2003, Plate 70). with midcircle of radius and at height can be represented parametrically by for and The coefficients of the first fundamental form for this surface are the second fundamental form coefficients are the area element is and the Gaussian and mean curvatures are from to , which can unfortunately not be done in closed form. Note that although the

10. Moebius Strip - Flash And VRML Presentation This flash movie includes information about the moebius strip, who invented it, and how to construct one all presented in an interactive way that is http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. 3Dgate.com - Your Source For All That Is 3D Thru the moebius strip Preproduction http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

12. Thru The Moebius Strip - The Movie http://www.moebiusstrip.net/

13. Flexagons And Kaleidocycles, Also Moebius Strip Flexagons and Kaleidocycles, also moebius strip http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

14. Thru The Moebius Strip - The Movie This is a story about the coming of age of a brave, resourceful 14 year old boywho grew up refusing to accept the loss of his father. http://www.moebiusstrip.net/html/

15. Chess In A Moebius Strip 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? http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

16. Moebius How to make a moebius strip. 1. Take a strip of paper. 2. Give it a half twist (turn one end over). 3. Tape the ends together. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

17. UM-VRL: Moebius Strip In VRML A virtual reality model (VRML) of the moebius strip with an animated processionof balls moving in an endless loop along this unique onesided surface. http://www-vrl.umich.edu/project2/moebius/

The Moebius Strip in VRML The mathematician A. F. Moebius (1790-1886) discovered this one-sided surface that became known as the Moebius Strip or Moebius Band. The artists M. C. Escher (1898-1972) was intrigued by the strip's puzzling geometry and included a procession of ants crawling along a Moebius Band in his collection of drawings depicting spatial illusions. The Moebius Strip, however, is not an illusion. It can be modeled in 3D and its topological features can be explored using an interactive computer model. Inspired by Escher's work, Bert Schoenwaelder created this unique VRML application with an animated procession of balls during his internship at the University of Michigan Virtual Reality Laboratory. Escher Schoenwaelder Main Features A simple endless band in the form of belt-shaped loop (below left) has two distinct surfaces and two edges. Moving from one surface to the opposite site requires crossing one of the edges. The Moebius Strip is an endless band that includes a half twist (below right). Amazingly, the band has only one surface and only one edge. Moving along the surface (like Escher's ants) will bring you to the opposite site without crossing the edge. simple endless band load VRML endless band with half twist load VRML Explore the Animated Model Load the VRML Animation (11.0K) of the Moebius Strip

18. China Works Up A 3-D Challenge aiming for the big time with the worldwide release of its first 3D feature film, "Thru the moebius strip " a science-fiction adventure about http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

19. UM-VRL: Moebius Strip 2 click to enlarge to screen size. http://www-vrl.umich.edu/project2/moebius/scrx.html

click to enlarge to screen size click to enlarge to screen size

20. Thru The Moebius Strip (2005) Thru the moebius strip Cast, Crew, Reviews, Plot Summary, Comments, Discussion,Taglines, Trailers, Posters, Photos, Showtimes, Link to Official Site, http://www.imdb.com/title/tt0267024/

Home Top Movies Photos Independent Film ... Register to personalize All Titles My Movies Names Companies Keywords Characters Quotes Bios Plots More searches Tips IMDbPro.com free trial Showing page 1 of 12 main details combined details full cast and crew company credits user comments external reviews newsgroup reviews user ratings recommendations plot summary plot keywords Amazon.com summary memorable quotes trivia goofs soundtrack listing crazy credits alternate versions movie connections merchandising links release dates filming locations technical specs laserdisc details DVD details literature listings news articles taglines trailers posters photo gallery on tv, schedule links showtimes official site miscellaneous photographs sound clip(s) video clip(s) Your Vote 1 (awful) 10 (excellent) You need to be a registered user of the IMDb to rate a movie - I have seen this movie and would like to submit a comment Thru the Moebius Strip Directed by Glenn Chaika Writing credits Jean Giraud (story) Add to MyMovies Photos IMDbPro Professional Details Genre: Animation Adventure Sci-Fi Plot Outline: In the not-too-distant future, a young boy travels to an alien world to find his father and learn of his destiny.

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