An article of clothing and a ray of sunshine: making uncountable nouns countable 2. Definitions Clear explanations of natural written and spoken English.

## Möbius strip

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The word in the example sentence does not match the entry word. The sentence contains offensive content. Cancel Submit. Your feedback will be reviewed. Geometrical shapes. Browse mobilization. Test your vocabulary with our fun image quizzes. Image credits. Word of the Day safari park.It can be made using a strip of paper by gluing the two ends together with a half-twist. 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.

The parameter u runs around the strip while v moves from one edge to the other. It is a standard example of a surface which is not orientable. Such belts last longer because the entire surface area of the belt gets the same amount of wear. There, they allow the ribbon to be twice as wide as the print head while using both half-edges evenly. Nikola Tesla patented similar technology in the early s: [5] "Coil for Electro Magnets" was intended for use with his system of global transmission of electricity without wires.

From Simple English Wikipedia, the free encyclopedia. In: Naturwissenschaftliche Rundschau Wissenschaftliche Verlagsgesellschaft, p. Pickover March Thunder's Mouth Press. Naturwissenschaftliche Rundschau. ISSN Lynch on Lynch. London, Boston. Microwave Theory and Tech. Patent 3.

## The Mathematical Madness of Möbius Strips and Other One-Sided Objects

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### Möbius Strips – Meaning, Origin and Symbolism

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This article has been viewed 98, times. Learn more The magic circle, or Mobius strip, named after a German mathematician, is a loop with only one surface and no boundaries. If an ant were to crawl along the surface of the Mobius strip, it would walk along both the bottom and the top in an infinite loop. You can easily construct and experiment with a Mobius strip using paper, scissors, tape, and a pencil.

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Log in Social login does not work in incognito and private browsers. Please log in with your username or email to continue. No account yet? Create an account. Edit this Article. We use cookies to make wikiHow great. By using our site, you agree to our cookie policy. Cookie Settings. Learn why people trust wikiHow. Download Article Explore this Article parts. Things You'll Need. Related Articles.It can be realized as a ruled surface.

For example, any rectangle can be glued left-edge to right-edge with a reversal of orientation. Some, but not all, of these can be smoothly modeled as surfaces in Euclidean space. Such paper models are developable surfaces having zero Gaussian curvatureand can be described by differential-algebraic equations.

A line drawn along the edge travels in a full circle to a point opposite the starting point. If continued, the line returns to the starting point, and is double the length of the original strip: this single continuous curve traverses the entire boundary. This happens because the original strip only has one edge, twice as long as the original strip.

Cutting creates a second independent edge of the same length, half on each side of the scissors. Cutting this new, longer, strip down the middle creates two strips wound around each other, each with two full twists. The other is a thin strip with two full twists, a neighborhood of the edge of the original strip, with twice the length of the original strip. Other analogous strips can be obtained by similarly joining strips with two or more half-twists in them instead of one.

For example, a strip with three half-twists, when divided lengthwise, becomes a twisted strip tied in a trefoil knot. If this knot is unravelled, the strip has eight half-twists. The parameter u runs around the strip while v moves from one edge to the other. For a smaller aspect ratio, it is not known whether a smooth embedding is possible. This folded strip, three times as long as it is wide, would be long enough to then join at the ends.

This method works in principle, but becomes impractical after sufficiently many folds, if paper is used. Using normal paper, this construction can be folded flatwith all the layers of the paper in a single plane, but mathematically, whether this is possible without stretching the surface of the rectangle is not clear.

It is a standard example of a surface that is not orientable. It may be constructed as a surface of constant positive, negative, or zero Gaussian curvature. But there is no metric on the space of lines in the plane that is invariant under the action of this group of homeomorphisms.

### Möbius strip

In this sense, the space of lines in the plane has no natural metric on it.He likely encountered the concept while he was working on the geometric theory of polyhedra, a three-dimensional object made of a polygon. This made August Mobius the first in the race and so the symbol was named after him. In an ordinary two-sided loop with an inside and outsidean ant could crawl from the starting point and reach the ends only onceeither on the top or the bottom—but not on both sides.

Most people become fascinated when the strip is split into halves. Typically, cutting an ordinary two-sided strip along the center will result in two strips of the same length. This video very beautifully demonstrates these concepts. Here are some of figurative interpretations on the symbol:.

The discovery of the Mobius strip led to new ways of studying the natural world, especially topologya branch of mathematics that deals with the properties of a geometric object unaffected by deformations. The Mobius strip inspired the concept of the Klein bottle with one side, which cannot hold a liquid since there is no inside or outside.

The concept of mathematical infinity began with the Greeks around 6th century B. While it might have been present in earlier civilizations of the Egyptians, the Babylonians, and the Chinese, most of these cultures dealt with its practicality in daily life—not the concept of infinity itself. Eventually, he became an advocate of using mathematics as a framework of art.

Insegnante educazione fisica laurea triennaleThe concept of the strip is also evident in works of Maurits C. Escher, a Dutch graphic artist who is famous for designing mathematically inspired prints, such as mezzotints, lithographs, and woodcuts. He created the Mobius Strip I infeaturing a pair of abstract creatures chasing each other; and the Mobius Strip II — Red Ants inwhich depicts ants climbing the infinite ladder.

Inhe created the Horsemenportraying two groups of horses marching around the strips endlessly. In addition, the depiction itself connected the sides of the strip to let the two teams of horsemen meet. It was used in typewriter ribbons and recording tapes too, and is commonly found on various packaging as a symbol for recycling. In jewelry design, the motif is popular in earrings, necklaces, bracelets, and wedding rings.

Some are designed with words inscribed on silver or gold, while others are studded with gemstones.

Ceramiche darte elegance white onyx tileThe symbolism of the piece makes it an attractive design, especially as a gift for loved ones and friends. The symbol has also become a popular style for scarves in various materials and prints, as well as tattoos. The Mobius strip has many practical applications in the fields of science and technology, as well as an inspiration in fashion, jewelry design, and pop culture.

Privacy Policy. Terms of Use. Religious Symbols. Egyptian Mythology. Japanese Mythology. Affiliate Disclosure.You have most likely encountered one-sided objects hundreds of times in your daily life — like the universal symbol for recycling, found printed on the backs of aluminum cans and plastic bottles. This mathematical object is called a Mobius strip. Another mathematician named Listing actually described it a few months earlier, but did not publish his work until The concept of a one-sided object inspired artists like Dutch graphic designer M.

For instance, try taking a pair of scissors and cutting the strip in half along the line you just drew. While the strip certainly has visual appeal, its greatest impact has been in mathematics, where it helped to spur on the development of an entire field called topology.

A topologist studies properties of objects that are preserved when moved, bent, stretched or twisted, without cutting or gluing parts together. For example, a tangled pair of earbuds is in a topological sense the same as an untangled pair of earbuds, because changing one into the other requires only moving, bending and twisting.

No cutting or gluing is required to transform between them. Another pair of objects that are topologically the same are a coffee cup and a doughnut. Because both objects have just one hole, one can be deformed into the other through just stretching and bending. The number of holes in an object is a property which can be changed only through cutting or gluing. Imagine writing yourself a note on a see-through surface, then taking a walk around on that surface.

Sql date format yyyymmdd javaThe surface is orientable if, when you come back from your walk, you can always read the note. On a nonorientable surface, you may come back from your walk only to find that the words you wrote have apparently turned into their mirror image and can be read only from right to left.

**Klein Bottles - Numberphile**

On the two-sided loop, the note will always read from left to right, no matter where your journey took you. When the GIF starts, the dots listed off clockwise are black, blue and red.

This transformation is impossible on an orientable surface like the two-sided loop. The concept of orientability has important implications. Take enantiomers.

Crooked tongues websiteThese chemical compounds have the same chemical structures except for one key difference: They are mirror images of one another. For example, the chemical L-methamphetamine is an ingredient in Vicks Vapor Inhalers.

Its mirror image, D-methamphetamine, is a Class A illegal drug. If we lived in a nonorientable world, these chemicals would be indistinguishable. The study of topology continues to produce stunning results. For example, last year, topology led scientists to discover strange new states of matter. David Gunderman, Ph. Continue or Give a Gift. Privacy Terms of Use Sign up. SmartNews History. History Archaeology. World History.

Science Age of Humans. Future of Space Exploration. Human Behavior. Our Planet. Earth Optimism Summit. Ingenuity Ingenuity Awards.This space exhibits interesting properties, such as having only one side and remaining in one piece when split down the middle. See also Klein bottle. Print Cite verified Cite.

While every effort has been made to follow citation style rules, there may be some discrepancies. Please refer to the appropriate style manual or other sources if you have any questions.

Facebook Twitter. Give Feedback External Websites. Let us know if you have suggestions to improve this article requires login. External Websites. The Editors of Encyclopaedia Britannica Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree See Article History. Britannica Quiz. All About Math Quiz. Your algebra teacher was right.

You will use math after graduation—for this quiz! See what you remember from school, and maybe learn a few new facts in the process. Learn More in these related Britannica articles:. Both spaces can be thought of as one-dimensional…. The German mathematician Johann Benedict Listing had discovered it a few months earlier, but he did not publish his discovery until History at your fingertips. Sign up here to see what happened On This Dayevery day in your inbox! Email address. By signing up, you agree to our Privacy Notice.

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