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Möbius strip

23.5k Caesarblack  7.3 years ago
1,051 downloads

The Möbius strip or Möbius band ( (non-rhotic) or ; German: ['mø?bi??s]), also spelled Mobius or Moebius, is a surface with only one side (when embedded in three-dimensional Euclidean space) and only one boundary. The Möbius strip has the mathematical property of being unorientable. It can be realized as a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858.

An example of a Möbius strip can be created by taking a paper strip and giving it a half-twist, and then joining the ends of the strip to form a loop. However, the Möbius strip is not a surface of only one exact size and shape, such as the half-twisted paper strip depicted in the illustration. Rather, mathematicians refer to the closed Möbius band as any surface that is homeomorphic to this strip. Its boundary is a simple closed curve, i.e., homeomorphic to a circle. This allows for a very wide variety of geometric versions of the Möbius band as surfaces each having a definite size and shape. For example, any rectangle can be glued to itself (by identifying one edge with the opposite edge after a reversal of orientation) to make a Möbius band. Some of these can be smoothly modeled in Euclidean space, and others cannot.

A half-twist clockwise gives an embedding of the Möbius strip different from that of a half-twist counterclockwise – that is, as an embedded object in Euclidean space, the Möbius strip is a chiral object with right- or left-handedness. However, the underlying topological spaces within the Möbius strip are homeomorphic in each case. An infinite number of topologically different embeddings of the same topological space into three-dimensional space exist, as the Möbius strip can also be formed by twisting the strip an odd number of times greater than one, or by knotting and twisting the strip, before joining its ends. The complete open Möbius band is an example of a topological surface that is closely related to the standard Möbius strip, but that is not homeomorphic to it.

Spotlights

General Characteristics

  • Created On Windows
  • Wingspan 22.8ft (6.9m)
  • Length 22.0ft (6.7m)
  • Height 22.6ft (6.9m)
  • Empty Weight 4,663lbs (2,115kg)
  • Loaded Weight 4,663lbs (2,115kg)

Performance

  • Wing Loading N/A
  • Wing Area 0.0ft2 (0.0m2)
  • Drag Points 5509

Parts

  • Number of Parts 361
  • Control Surfaces 0
  • Performance Cost 868
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  • Profile image
    1,524 Jayv210

    True @Caesarblack

    7.2 years ago
  • Profile image
    23.5k Caesarblack

    @Jayv210 lol but it's a bit hard to make it with simpleplane :p

    7.3 years ago
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    1,524 Jayv210

    You should make a klien bottle now (basically a three dimensional version of a Möbius strip)

    7.3 years ago
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    reading this make me confused

    7.3 years ago
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    11.1k JetWondy

    @Haydencal wut M8?

    7.3 years ago
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    19.5k ACMECo1940

    How was the conjured

    7.3 years ago
  • Profile image
    23.5k Caesarblack

    @FlipposMC It's too hard for me QAQ

    7.3 years ago
  • Profile image
    12.6k Flippos

    How about a Klein bottle?

    7.3 years ago
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    12.6k Flippos

    @iwannabeelected kek, I made a hypercube but it's not nearly as amazing as this is.

    7.3 years ago
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    14.8k Cadillace

    It's REALLY amazing......

    7.3 years ago
  • Profile image
    23.5k Caesarblack

    @GA2002 😂

    7.3 years ago
  • Profile image
    4,353 GA2002

    @Caesarblack 看着玩🙃

    7.3 years ago
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    2,100 FgFg

    I totally agree @Stellarlabs, my mind was blown as hard when I realized unfrosted pop tarts have 10 more calories than frosted pop tarts (plain ones that is) @Caesarblack

    7.3 years ago
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    36.2k DbE

    my brain hurts... but then i do study time.. and that hurts my brain too.

    7.3 years ago
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    23.5k Caesarblack

    @iwannabeelected Good idea....But I can't make a 4 dimensional object in 3 dimensions space QAQ

    7.3 years ago
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    23.5k Caesarblack

    @LockOn thanks(:з」∠)

    7.3 years ago
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    Hey, how about a Hypercube?

    7.3 years ago
  • Profile image

    Whoa, cool

    7.3 years ago
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    2,781 LockOn

    666,很美的一个几何体!

    7.3 years ago
  • Profile image
    23.5k Caesarblack

    @GA2002 沒啥用

    7.3 years ago
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    23.5k Caesarblack

    @Flightsonic It's.... Maybe too hard for me to build QAQ

    7.3 years ago
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    4,353 GA2002

    。。。。。有啥用么

    7.3 years ago
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    23.5k Caesarblack

    @Aarons123 Yes it is pure math XD

    7.3 years ago
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    16.2k Mox

    Spoopy

    7.3 years ago
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    Nice bro, i love these things

    7.3 years ago
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