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1. Möbius Strip -- From MathWorld
html. Escher, M. C. moebius strip I. Wood engraving and woodcutin red, green, gold and black, printed from 4 blocks. 1961. http
http://mathworld.wolfram.com/MoebiusStrip.html

Extractions: MATHWORLD - IN PRINT Order book from Amazon Geometry Surfaces Miscellaneous Surfaces ... cylinder , it is not a true surface, but rather a surface with boundary (Henle 1994, p. 110). Euler characteristic 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). w with midcircle of radius R and at height z = can be represented parametrically by

2. Moebius Strip
moebius strip A moebius strip is a onesided 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.
http://zebu.uoregon.edu/~js/glossary/moebius_strip.html

Extractions: 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.

3. The Shrine Of Escher, Art Gallery
moebius strip. moebius strip II, woodcut, printed from 3 blocks. 1963, 45x20 cm. A moebius strip is a surface that has only one surface, as it is attached to itself and twisted halfway around. Thus
http://www.uvm.edu/~mstorer/escher/moebius.html

4. Moebius Strip
moebius strip. Sphere has two sides. A bug may be trapped Escher (18981972).To obtain a moebius strip, start with a strip of paper. Twist one
http://www.cut-the-knot.org/do_you_know/moebius.shtml

Extractions: Recommend this site Moebius Strip 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 A. F. Moebius (1790-1868) and bears his name. Sometimes it's alternatively called a Moebius band. (In truth, the surface was described independently and earlier by two months by another German mathematician J. B. Listing .) The strip was immortalized by M. C. Escher To obtain a Moebius strip, start with a 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 of a twisting Moebius strip. (When you get to the movie page click on the frame to start the movie.)

5. Moebius Strip
moebius strip, what is it, see an avi movie To obtain a moebius strip, start with a strip of paper Creating a moebius strip is a 3dimensional affair
http://www.cut-the-knot.com/do_you_know/moebius.html

Extractions: Recommend this site Moebius Strip 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 A. F. Moebius (1790-1868) and bears his name. Sometimes it's alternatively called a Moebius band. (In truth, the surface was described independently and earlier by two months by another German mathematician J. B. Listing .) The strip was immortalized by M. C. Escher To obtain a Moebius strip, start with a 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 of a twisting Moebius strip. (When you get to the movie page click on the frame to start the movie.)

6. Moebius Strip
Here is an interesting thing to do with 2 Möbius strips. (That is if your stipsare of equal length.) Now do the same again, but this time twist one strip.
http://www.cut-the-knot.org/do_you_know/moebius2.shtml

Extractions: 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!

7. Moebius
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.
http://mathforum.com/sum95/math_and/moebius/moebius.html

Extractions: A moebius strip is a loop of paper with a half twist in it. 1. Take a strip of paper. 2. Give it a half twist (turn one end over). 3. Tape the ends together. 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. 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? 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...

8. Moebius
The moebius strip. A moebius strip is a loop of paper with a half twistin it. How to make a moebius strip. 1. Take a strip of paper.
http://mathforum.org/sum95/math_and/moebius/moebius.html

Extractions: A moebius strip is a loop of paper with a half twist in it. 1. Take a strip of paper. 2. Give it a half twist (turn one end over). 3. Tape the ends together. 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. 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? 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...

9. Math Forum: Mathematics And... - Jan Garner
Mathematics and by Jan Garner. Back to sum95 Projects Page Forum Web Units.Art. Perspective Drawing. Things to make. The moebius strip. Polyhedra. Spreadsheets.
http://mathforum.org/sum95/math_and/

10. Graphics Archive - Flat Moebius Strip By Henry Rowley
Special TopicsTopology. Flat moebius strip by Henry Rowley. This moebius strip is isometric to a flat rectangle, which differs from the standard parametrization.
http://www.geom.umn.edu/graphics/pix/Special_Topics/Topology/moebius_strip.html

Extractions: Graphics Archive Up Comments 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

11. 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/

Extractions: 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. 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.

12. Starting Thru The Moebius Strip The Movie
detecting flash player To visit the flash version ofThru The moebius strip, Flash Player 7 is required.
http://www.moebiusstrip.net/

13. Thru The Moebius Strip - The Movie
http://www.moebiusstrip.net/start.htm

14. The Moebius Strip
The moebius strip Arnita Newton Kenwood Academy 4800 Chicago Beach Drive 5015 BlackstoneAvenue Chicago IL 60615 Chicago IL 60615 312548-1446 312-535-1350
http://www.iit.edu/~smile/ma9113.html

Extractions: 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

15. 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

Extractions: Graphics Archive Up Comments 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

16. LookSmart - Directory - Thru The Moebius Strip
Thru the moebius strip Learn about the production of the animatedscience-fiction film from the mind of Jean Moebius Giraud.
http://search.looksmart.com/p/browse/us1/us317828/us317854/us164424/us270941/us9

17. Chess In A Moebius Strip
http://www.chessvariants.com/shape.dir/x_moeb.html

18. Moebius Chess
where you started to draw. A Moebius Chess Board. The chess boardof Moebius Chess is like a moebius strip. The idea is consider
http://www.chessvariants.com/shape.dir/moebius.html