Geometry.Net - Math_Discover: Moebius Strip

Moebius Strip
evolutie's site math - geometry - moebius strip. geometry.
http://www.evolutie.demon.nl/math/geometry/Moebius.htm
Moebius Strip
evolutie's site stuff - moebius strip. stuff.
http://www.evolutie.demon.nl/stuff/10032001a.htm
Lycos Tripod Homepages - Gratis Hosting
Moebius' Strip top If, however, you turn one end of another strip and gluethe ends, the result is the socalled 'moebius strip' on the right.
http://mitglied.lycos.de/jkoeller/strip.html
Moebius Strip
The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set.
http://163.15.59.77/butiful/moebius.htm

Extractions: (Moebius Strip) ¦pªG ²ö¤ñ±a ¥u»Ý±N¤@±i¯È±øªº¤@ä§áÂà180«×«á¡AÂH¶K¦b¥t¤@ä¤W ¡C²ö¤ñ±a³Ì«nªº©Ê½è¬O¥u¦³¤@±©M¥u¦³¤@ä¡C¦pªG§ÚÌ±N¤@±i¯È±øªº¤@ä¦P¤è¦V§áÂà180«×¤G¦¸©Î¤T¦¸...........«á¡AÂH¶K¦b¥t¤@ä¤W,¤´¬O¤@±ø²ö¤ñ±a¡C ¦pªGªu±a¼e¤G¤À¤§¤@³B,¾î°Å¤@©P,±o¨ì§á¤GÂàªº±a¤l,¥¦¦³¤G± ,¦ý¤£¬O²ö¤ñ±a. ¦pªGªu±a¼e¤T¤À¤§¤@³B,¾î°Å¤@©P,±o¨ì¬Û¦©ªº¤G±ø±a¤l,¨ä¤@¬O²ö¤ñ±a,ªø«×©Mì¨Ó¬Û¦P,¼e«×¬Oì¨Óªº¤T¤À¤§¤@¡C¥t¤@±ø¸ûªøªº±a¤l¬O¤G±ªº±a¤l,ªø«×¬Oì¨Óªº¤G¿,¼e«×¬Oì¨Óªº¤T¤À¤§¤@.
Marvellous Moebius Molecule
worked out how to form ring molecules, they also realised that they could makea special set of ring molecules that had the same shape as a moebius strip.
http://www.mathemagic.org/MOBM/moebiusmolecules.html

Extractions: Marvellous moebius molecules and other shapes Certain types of large ring-shaped molecules or 'cyclic polymers' can be made in the laboratory. These molecules have some fascinating and unexpected properties, suggesting some useful applications. For example silicon polymers are used as lubricating oils. Cyclic versions of the polymers freeze at lower temperatures than linear ones of the same mass. So if you were on an expedition to the Antarctic you might find some cyclic polymers being used to stop your vehicle freezing up. When chemists worked out how to form ring molecules, they also realised that they could make a special set of ring molecules that had the same shape as a moebius strip. What is special about their shape? Moebius molecules are made from a loop with a single half twist in it this means that the loop only has one side and that's what gives it its special properties. Try out some Moebius magic by following the instructions below.
Abstract And Geometric Acrylics And Oil Paintings : Marcellux' Art Gallery
Self Portrait (Digital Art). moebius strip serial. moebius strip The neverendingpath, the road to nowhere, the vicious circle. You finish where you begin.
http://marcellux.tripod.com/moebius/

Extractions: M arcellux.- Visual Artist Self -Portrait (Digital Art) " Moebius Strip " serial Moebius Strip: The neverending path, the road to nowhere, the vicious circle. You finish where you begin. You advance just to reach the point where you started. A mess done for nothing... All your effort is worthless. The ethernal searching of what you've always had with you... What a powerful concept!, How many amazing histories to tell... Could I resist such a temptation? Not at all. As everybody I know, I have experienced the atraction of the Moebius Strip... Here I share it with you. Enjoy yourselves... Marcellux This serial is still in process!! I'm still making it. Here you have the chance to see how a serial is made Moebius Strip #1 Oil on canvas 19" x 27" Moebius Strip #2 Oil on canvas 19" x 27" Click to enlarge Click to enlarge Would you like to see MORE Paintings? Bonus!!! Download Free Wall papers of Marcellux paintings Download To mail the Curator of this page and ask information about Marcellux' work Click Here Last Update: Year 2002 Counter:
Moebius Strip Scarf
moebius strip Scarf. price $3.95 A moebius strip has only one surfaceand one edge.While normal way to make a moebius is to knit
http://store.carodanfarm.com/skuac39.html

Extractions: price: $3.95 A Moebius strip has only one surface and one edge.While normal way to make a moebius is to knit a rectangle, give it a half twist, join the ends, these instructions have you cast on in manner that will automatically generate the half twist. Fingering wt. To choose this item, select the appropriate options (if any) and click "Add to Cart".
Paper Moebius Bands
Keep cutting along the moebius strip until you return to the place where youbegan. Observe what happens this time. Which band is a moebius strip?
http://nths.newtrier.k12.il.us/academics/math/Connections/curves/moebpapr.htm

Extractions: New Trier High School, Winnetka, Illinois Paper Moebius Bands (Sorry! picture not yet available) Description: A Moebius "strip" or "band" is a loop which has been made by twisting a strip of paper 1/2 turn and taping the ends together. Our exhibit consists of supplies to make Moebius strips and perform experiments with them. The supplies include 2-1/8" by 14" paper strips cut from legal size copier paper, tape, scissors, and colored markers. Directions are given for the following two experiments: Experiment 1: a. Create a Moebius band by twisting the paper 1/2 turn and taping the ends together. b. Use a colored marker to mark a line down the middle of the strip. Continue until you come back to your starting point. Look to see whether your strip is marked on one side or both. c. Use scissors to cut the strip down the middle along your colored line. Observe what happens. d. Use a marker to mark a new line down the middle of your new strip. Continue until you come back to your starting point. Look to see whether your new strip is marked on one side or both. Experiment 2: a. Create a second Moebius band.
Moebius Ant Sculpture
A moebius strip is created by twisting a thin strip of paper onehalfturn and taping its ends together to form a shape similar to a figure eight.
http://nths.newtrier.k12.il.us/academics/math/Connections/curves/moebants.htm

Extractions: New Trier High School, Winnetka, Illinois Moebius Ant Sculpture Description: A Moebius strip is created by twisting a thin strip of paper one-half turn and taping its ends together to form a shape similar to a figure eight. It has the unique property that it has only a single surface; its front surface continues onto its back surface without going over an edge! One of M.C. Escher's famous etchings depicts a parade of ants marching along the continuous path of a moebius strip. Our exhibit consists of two parts as shown above: a mounted picture of Escher's Moebius etching a 3 foot long model of a moebius strip with a set of large plastic insects marching along the strip Purpose: Each individual exhibit in our collection of moebius strip exhibits is intended to encourage students to explore topological oddities and to become more aware of properties of 3-dimensional shapes in the world around them.This particular exhibit was created as an eye catcher which would call attention to the art of Escher and the concept of the Moebius bands. Topology is the study of shapes and their relationships. Moebius strips provide an interesting introduction to this broad subject.
Encyclopædia Britannica
Your search thru the moebius strip. Log In or Subscribe Now. Expand your searchon Thru the moebius strip with these databases Journals and magazines.
http://search.britannica.com/search?query=Thru the Moebius Strip
Moebius Strip
TITLE moebius strip AUTHOR Cherubino EMAIL mne@si.rr.com DISTRIBUTION Pleasecontact me first SPOILERS s2 - Ouroboros SHIP Tyr/F CONTENT Adult
http://www.thedrawlyn.com/sub/marsinleo/stories/cherubino/moebius.html

Extractions: DATE: April 19, 2002 Moebius Strip So all this uncertainty and indecisions had finally got me here. Where is here somewhere in the mostly snowy part of Europe where the Institute of Quantum and Temporal Mechanics took residence several years ago. I am their physician. I was their best field medic until I messed up that mission. Dura lex sed lex This boy is going to drive me to insanity! All I wanted to do was to get to my quarters and take a shower! Instead, I ended up almost blown out of the ship. And I hate Perseids! Finally the doors are locked and after I make it clear to Harper that I do not particularly care to be a subject in his experiments. I start walking, I have to find a way out of here, and I have to find some means of communication with Andromeda. It is freezing cold, I am bleeding and my body seems to be refusing to adapt to the sub-zero temperature, but I keep moving. I know if I stop I will die and that is unacceptable. I will not die in the snow in the middle of nowhere; it takes much more then that to kill Tyr Anasazi!
An Exploration Of Surfaces - Transformations
be clearer. moebius strip to Cross Cap with a Disk Removed. As mentionedin Half Klein Bottle to moebius strip. As a moebius strip is
http://www.math.arizona.edu/~rta/013/bethard.steven/transform.html

Extractions: Email Dr. Gay Often we find that two seemingly different surfaces are actually (at least in some topological sense) equivalent. This section provides animations of some of the more complicated transformations from one form of a surface to another. Below each animation is a description of the moves used to transform one projection of the surface to the other. (This section relies somewhat upon the Roseman Homma-Nagase moves. If you are unfamiliar with these moves, you should read The Basics For each of the transformations, we rendered the animation with two different textures. Generally, the wood texture is the more stable of the two (the striped texture sometimes moves in an unexpected manner), but for some transformations, the striped texture may be clearer. As mentioned in the Construction section, we can stretch the moebius strip around to make it resemble the cross cap with a single circular disk removed. In this animation, we place the edge of this disk in the plane where the cross cap would normally intersect itself. Striped
An Exploration Of Surfaces - Constructions
We then simply join the two ends of this cylinder together. Construction of a MoebiusStrip. The moebius strip is probably our simplest nonorientable surface.
http://www.math.arizona.edu/~rta/013/bethard.steven/construct.html

Extractions: Email Dr. Gay Each of the surfaces below is created by adjoining the edges of a square pattern (sometimes with a twist, sometimes without one). In the "Pattern" diagrams, we indicate this by coloring edges the same color if they need to meet each other (that is, gray meets gray, black meets black). Twists (or the lack thereof) are indicated by arrows on the edges - to correctly assemble the pattern, when the edges have been joined, arrows with the same color should point the same way. The sphere is the first of two orientable surfaces we will examine. While there are infinitely many representations of the sphere (as there are for any topological surface), we will use the most familiar one. Quicktime If you look at the square pattern for the sphere, you might notice that the left and top sides mirror the right and bottom sides. Because of this, we may actually think of this pattern as having only two sides (where the left-top is on side, and the right-bottom is the other). In this manner, we can then see that the sphere is constructed by simply joining each of the two sides of the pattern together without any twists. In the animation, we expand the surface downward, and then just align the two edges to meet each other. The torus or doughnut is our other orientable surface. In its standard representation, it looks just like one would expect a doughnut to look.
Music
If you are at all confused when going through our examples, just remembera moebius strip is a loop with a twist. moebius strip Tease.
http://www.carliner-remes.com/jacob/math/project/music.htm

Extractions: Preface for Teachers Introduction to Orientability: A Fable The Math of Non-Orientable Surfaces Surface and Manifold ... Bibliography 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! 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
Introduction: A Fable
it was Moebius. (The Lapaloopans evidently thought this had a nicering to it.) Soon after, The Strip became The moebius strip.
http://www.carliner-remes.com/jacob/math/project/intro.htm

Extractions: Preface for Teachers Introduction to Orientability: A Fable The Math of Non-Orientable Surfaces Surface and Manifold ... Bibliography Once upon a time, in a land that looked and seemed very much like yours and mine, there lived a plentiful race of people named the Lapaloopans who had ruled their world for many years. They called it The Strip , except there were no gambling casinos or bright neon lights. To the Lapaloopans, it was simply their home. The Strip had local movie theatres and local delicatessens just like our world, where the Lapaloopans went to eat and unwind. The Lapaloopan sun rose over the Lapaloopan horizon just as our Sun does, and, except for the mountains and hills, the Lapaloopan land was broad and flat, as far as the eye could see. All around, the Lapaloopans lived a happy, contended life. Things went very well on The Strip for many centuries. The Lapaloopans had built a straight and even white fence at the edge of their Lapaloopan border for the protection of the children. No Lapaloopan had ever been past the tall white spires of this fence, and that served them very well. No citizen of The Strip , young or old, had ever been lost, and everyone knew at all times where everyone else was, within the local territory.
Image Index
Image Index Klein Bottle moebius strip 1 moebius strip 2 moebius strip 3 moebius strip 4 Ring Knot Cutout Octahedron Three Rings Knot 2
http://www.scg.uwaterloo.ca/~hqle/WAVEFRONT/wfrntpics.html
Untitled Document
moebius strip is onesided surface. moebius strip I 1961 wood engraving and woodcutin red, green, gold and black, printed from 4 blocks. Making a moebius strip.
http://home.uchicago.edu/~arabbani/escher.htm

Extractions: Here is a picture by Maurice C. Eshcer. Moebius strip is one-sided surface. It 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 (1898-1972). Moebius Strip I 1961 wood engraving and woodcut in red, green, gold and black, printed from 4 blocks Making a Moebius Strip To obtain a Moebius strip, start with a strip of paper. Twist one end 180o (half turn) and glue the ends together. 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.
No Moebius Strip?
no moebius strip? This response submitted by fred davis on 11/24/97. Email Addressfddavis@utahiner.net Mike We are all changed by our experiences.
http://neuro-www.mgh.harvard.edu/forum/MoebiusSyndromeF/noMoebiusstrip.html
No-Sided Usenet
This is the amazing moebius strip. It has only one side. This twistgives the moebius strip amazing mathematical powers. Observe! .
http://world.std.com/~mmcirvin/kibology/moebius.html

Extractions: Home Humor from a.r.k Matt McIrvin mmcirvin@world.std.com kibo@world.std.com (James "Kibo" Parry) wrote: It's also interesting that Desiderio Alberto Arnaz y de Ancha IV is forty-six years old and yet he's only been in twelve hours of television, not counting the nine months before he was born when his mom was falling off ladders on TV every day. Curiously, in those twelve hours when he was on TV, in every single frame he had his mouth open and his eyes closed. Now, the average human being spends a total of twelve hours in that facial expression (blinking while yawning) during forty-six years, but by an amazing coincidence he happened to be on TV during those exact twelve hours. Clifton Fadiman printed this paragraph in his second sequel to "Fantasia Mathematica," "A Mathematical Mudbath." Only it was the original version that gave the surface area of a cube as pi r^3. It also reprinted my beloved tale of mathematical super-fiction, first published in High-Brow Science Fiction in 1953: SMEDLEY AND THE MOEBIUS DEBACLE By Dr. Matt "Longshot" McIrvin, Ph.D.
Zeal.com - United States - New - Entertainment - Movies - Movies By Genre - Anim
A great resource for United States New - Entertainment - Movies - Movies by Genre- Animation - Adventure - Thru the moebius strip. Thru the moebius strip
http://www.zeal.com/category/preview.jhtml?cid=10038169

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