The Moebius Strip

The Moebius Strip

You’ve probably heard the expression, “There are two sides to everything”. But are there? You can find out by making this strip.

Things you’ll need: several strips of paper 25cm long and 2cm wide, scissors, a pen, and tape.

1. To make the Moebius strip, you need to half-twist the strip of paper and tape the ends together. Now you have the Moebius strip.

2. Make some more Mobius strips. Then, cut one-half in the middle of the Moebius Strip with scissors as shown below. Oops! What happened?

3. Now cut a new strip one-third (1/3) just like the picture above but cut it 1/3.

The Möbius strip, Möbius band, Mobius or Moebius, is a surface with only one side and only one boundary. The Möbius strip has the mathematical property of being non-orientable. 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.

On 2. the Mobius strip will turn into a normal paper strip. On 3. the strip will turn into 2 paper bands!

6 Replies to “The Moebius Strip”

  1. Thank you for any other wonderful post. The place else may anybody get that type of information in such an ideal way of writing? I’ve a presentation next week, and I am at the look for such info.

  2. Doug Thomas – Alliance, NE – I retired from nearly 36 years in a factory that produces hydraulic and industrial hoses. That is the short of it. The most interesting thing I've done is serve in the US Army as a motion picture photographer. I was stationed in then-West Germany in Kaiserslautern, Kleber Kaserne, in the 69th Signal Company (Photo). I was sent all over western Europe filming military exercises and other less interesting things. This enabled me to become a "bier kenner", someone knowledgeable about beer. Haw! I was much younger then, and could handle the wear and tear. The most interesting thing that happened to me happened in 1980, the first day of the new year: I spotted a rara avis in my backyard. A phainopepla, a member of the silky flycatcher family! It stayed around for two months, long enough for me to photograph it through a garage window not more than 2m from a birdbath to which it came each day. The photos, sent to the state ornithological organization and their rare bird report committee, established me as the first and only person to have seen this particular bird in my state. Records for my state go back to Lewis and Clarke's western expedition, so that gives you the context and perspective through which other birders view my record. You should too! It was a once-in-a-lifetime occurrence. It lead to a decade of uninterrupted bliss, tracking down birds in the field with other people of a feather. The worst thing that happened to me is called Wegener's granulomatosis. Oh dear! This is where it becomes difficult! WG is a form of vasculitis that you have for life once it develops. It has no known cause, though scientists work as I write to try to determine why it occurs. My story is long and I am tired: More details later! It is a fatal disease without proper care. With proper care, people still can die! One last detail: a weggie (pronounced "wegg-ee"), is a person with Wegener's granulomatosis. It is an Australian construction, to the best of my knowledge, and suits me better than being known in perpetuity as a "WG patient". In 2016, a Wegener's flare mostly wiped out what kidney function I still had, and I went through a two month process of hospitalization and rehabilitation before I could return home to my two cats, Andy and Dougy. My neighbors across the lane took care of them while i was gone, with a childhood friend who substituted for my neighbors when they had to be out of town. The major change brought about by the flare: I now am on dialysis three times a week. Fortunately for me, my local general hospital has a very modern, well staffed dialysis unit. With a nurse-to-patient ratio of nearly one-one, it is the best of five dialysis sites I've been in. The recliners are even heated! Since these units are typically kept ice berg cold, you can see I feel like I am in heaven! (Well, not yet, but you get the idea!)
    weggieboy says:

    When this is applied to architecture, you get an interesting result!

    http://inhabitat.com/spectacular-lucky-knot-bridge-in-china-twists-and-turns-like-a-mobius-strip/

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