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In mathematics, a Möbius strip, Möbius band, or Möbius loop [a] is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and August Ferdinand Möbius in 1858, but it had already appeared in Roman mosaics from the third century CE .
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A Möbius strip with a geometric circle as boundary. The boundary has been highlighted in green, and a window cut in the fabric to show how the rope passes through. I sewed the model on January 29, 2005, and photographed it shortly afterwards.
A two-dimensional representation of the Klein bottle immersed in three-dimensional space. In mathematics, the Klein bottle (/ ˈ k l aɪ n /) is an example of a non-orientable surface; that is, informally, a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down.
The Möbius strip is a nontrivial bundle over the circle. Perhaps the simplest example of a nontrivial bundle E {\displaystyle E} is the Möbius strip . It has the circle that runs lengthwise along the center of the strip as a base B {\displaystyle B} and a line segment for the fiber F {\displaystyle F} , so the Möbius strip is a bundle of the ...
The logo is usually displayed with the arrows circulating clockwise, but the underlying Möbius strip exists in two topologically distinct mirror-image forms of opposite handedness. The American Paper Institute originally promoted four different variants of the recycling symbol for different purposes.
2005 saw the release of the Chinese movie Thru the Moebius Strip, based on a story by Giraud who also served as the production designer and the co-producer, and which reunited him with Arnie Wong, whereas his stint as concept designer on the 2012 animated science fiction movie Strange Frame, has become Giraud's final recorded motion picture ...
The alternative way of connecting the surfaces makes the "connection map" appear the same at both mouths. This configuration reverses the "handedness" or "chirality" of any objects passing through. If a spaceship pilot writes the word "IOTA" on the inside of their forward window, then, as the ship's nose passes through the wormhole and the ship's window intersects the surface, an observer at ...