Mobius Strip

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About: I like to make stuff and to make things work my way.

Intro: Mobius Strip

A Mobius strip is one of those interesting things for which there is little use other than starting an argument :-)

You need
- paper (ideally construction or other thick paper)
- scissors
- ruler

It should take about 10 minutes.

Step 1: Cut a Strip Off Paper

Cut a reasonably straight, parallel strip of paper. I cut about 3/4"(~1.5cm) off the long edge of a piece of letter size (~A4) bristol board paper, which worked well.
It isn't important how wide the piece is, but you want to get the long edges reasonable parallel, especially at the ends so the widths line up for the next step.

Step 2: Prep to Join the Narrow Edges Together

Hold the strip of paper with the two edges lining up with each other. Cut from about 1" (2.5cm) toward the opposite corner. The distance isn't important, but you want to have teh pieces held tightly together so they are cut the same, and you want to cut the line as straight as possible. This should leave you with a tapering end.

Cutting the end this way will
a) insure you tape the strip together right, and
b) make the connecting section stiffer, providing something similar to a "scarf joint" in woodworking.

Step 3: Tape the Ends Together

Put a piece of tape on one of the ends following the diagonal edge.
Hold the piece with the tape side up, and hold the other end on the other side of it. Flip over one end so the diagonal edges line up. Put the two ends as close together as possible and stick the loose end on the tape.
Add another piece of tape on the other side.

Step 4: Now What?

Well, your Mobius strip is done. Note how it only has one side. Yes, one, not two. (Unless you want to count the thickness of the paper, but that isn't really the point...)
To show it really only has one side, put a pencil on a spot anywhere along the strip and keep drawing in one direction. You will end up where you started. Now that couldn't be if it had two sides, right?
There is more fun to be had if you now cut along the line you just drew, because you will not end up with two strips.

For more info, check out the entry for Mobius Strip on Wikipedia.

Some of Escher's drawings are also based on this concept.

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    33 Discussions

    FINALLY! I found a one-sided 3-dimensional representation of a 2-dimensional object!

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    megziewoodles

    11 years ago on Introduction

    Awesome! If you make two mobius strips and stick them together at right angles and then cut each one up the middle you can make interlocking love hearts.

    2 replies
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    frank26080115

    11 years ago

    since it can be twisted any odd number of times and be any length, who wants to make the world's largest one sided object? or did somebody do that already?

    3 replies
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    berserkfrank26080115

    Reply 10 years ago on Introduction

    Actually, it can't be twisted just any number of times. If it's twisted more than once, you no longer have a mobius. For example, it would not act the same if you cut it in half lengthwise. Kinda freaky, I am glad I don't have to do the math for it.

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    berserkfrank26080115

    Reply 10 years ago on Introduction

    Hah! You got me there. You are right, of course, I had read it as the not so mathematical version of odd.

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    berserkshooter129

    Reply 10 years ago on Introduction

    Can you be more specific? I am only qualified for some kinds of help, but might be able to refer you to someone else for others ;-)

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    shooter129

    10 years ago on Introduction

    this is confuzzling i dont get it it feels like my brain is bleeding

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    ODC

    11 years ago

    I just created a user account to tell you all that Mobius strips arent as useless as you may think. They are used in many applications where a drive belt (from one pulley to another) is used. They are useful because they wear out each side more evenly than a normal belt. support the fair go for Mobius strips