Introduction: Mobius Strip

Picture of 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

Picture of 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

Picture of 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

Picture of 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?

Picture of 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.

Comments

nutsandbolts_64 (author)2011-04-11

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

megziewoodles (author)2007-06-27

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.

The SYNer (author)megziewoodles2010-03-29

If you make two mobius strips and attach them at the edges you make a

KLIEN BOTTLE!!!!!!!!!!!!!!!!!!!!!!!

en.wikipedia.org/wiki/Klien_bottle

Saturn V (author)The SYNer2010-11-10

Thanks for the link! You made my head explode!

gaby99 (author)2007-12-14

i looked at the picture for like 5 seconds and BAM! my head exploded

Saturn V (author)gaby992010-11-10

Sounds painful.

foxtrot4697 (author)gaby992008-11-02

same for me but first there was a ? mark over my head hitting me

frank26080115 (author)2007-01-20

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?

berserk (author)frank260801152007-12-15

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.

frank26080115 (author)berserk2007-12-15

"any >>odd<< number"

berserk (author)frank260801152007-12-16

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

shooter129 (author)2007-12-02

Nevamind

shooter129 (author)2007-11-30

HELP!!!

berserk (author)shooter1292007-12-01

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 ;-)

shooter129 (author)2007-11-30

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

aiden120000 (author)2007-01-21

mmm choclate on one side vanlilla on the other!

Vendigroth (author)aiden1200002007-06-10

but both sides are the same side(s)! unless you want chocolate-y vanilla-y impossible

aiden120000 (author)Vendigroth2007-06-12

it was a refrence to the simpsons. in the epsiode where it went all 3d

Vendigroth (author)aiden1200002007-06-12

lol srry, didn't catch that one

ODC (author)2007-02-20

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

berserk (author)ODC2007-03-08

That's a cool idea. I have never seen it happen. Do you have a picture or link?

twisted (author)2007-02-26

This makes me happy. 1 sided shapes will one day rule the world.

slyfox117 (author)2007-01-28

10 minutes? just take a strip of paper, twist, tape. nice instructable though.

uzerzero (author)2007-01-24

These are a great party conversation item, especially if someone at the party is high. They will be absolutely amazed at how this works. Great for laughs, also good for just simple amazement in sober people.

Mr. Smart Kid (author)2007-01-23

what does it do

berserk (author)Mr. Smart Kid2007-01-24

It doesn't do much, but what it does is not what you might expect. Check out Step 4, or the Wikipedia article it links to. Hard to describe, you sort of have to try it.

crestind (author)2007-01-21

These are pretty neat. They supposedly represent the maximum number of wormholes from point A to B or something like that.

Jezza Bear (author)2007-01-21

I love Mobius strips... now try this limerick A mathematician confided That a Möbius band is one-sided, And you'll get quite a laugh, If you cut one in half, For it stays in one piece when divided. See what happens when you cut it in half?!!!!! Now do it again but this time put TWO twists in it and then cut it in half....crazy. Welcome to the world of topology and Escher

Mr.Devious (author)2007-01-21

Sigh.."Coming up next, how to fold an anarchist ring and kill yourself"

bigpinecone (author)2007-01-20

THESE THINGS ROCK
i was at the mall once and the guy at the popcorn stand had 'em and cut one in half but it was still a ring =O

trebuchet03 (author)2007-01-20

ahh -- the classic riddle... "What has two edges and one side?" A Mobius of course :P

berserk (author)trebuchet032007-01-20

It has only one edge, though.

trebuchet03 (author)berserk2007-01-20

slaps hand on head :P how did I F that one up :P

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