How To Draw A Mobius Strip

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The magic circle, or Mobius strip, named after a German mathematician, is a loop with only one surface and no boundaries.^[one] A Mobius strip tin can come in whatsoever shape and size. If an emmet were to crawl forth the surface of the Mobius strip, it would walk along both the bottom and the top in an infinite loop. You can easily construct and experiment with a Mobius strip using paper, scissors, tape, and a pencil.

one
Cutting a strip of paper about 6 inches (15 cm) long and i.5 inches (3.eight cm) in width. When cutting the strip, the measurements exercise non need to be accurate, these are but suggested. Try to keep the width nonetheless that you lot have a long thin rectangle.
- To simplify the process, y'all tin can simply cutting downwards the edge of a apparently sheet of paper to make your strip.
2
Label the corners of the strip A, B, C, and D. In the meridian left corner of the strip, write a small letter A; in the meridian correct corner, write a pocket-sized B; the bottom left, the letter C; and the bottom right, the letter D. You volition apply these messages to marshal the strip after the twist.
- The size yous make the letters doesn't affair, but the position of each one is important for the twist pace.
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iii
Twist the A-C side a one-half turn and bring it to the B-D side. Hold the ii ends in your hands, requite the A-C side of the strip a half twist and join it to the B-D side. Lucifer the messages, A to D and B to C and tape the edges together. Once the edges are taped, y'all have completed the Mobius strip.
- You tin twist the newspaper more than than ane time and nonetheless have a Mobius strip.^[2]
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1
Depict a line along the middle of the strip. Using a pen or pencil, first at any point in the middle of the strip and draw a line all the way around without lifting your pen. Eventually, the pen will finish up dorsum at the point you started cartoon. Yous take drawn a line on both sides of the loop - merely without lifting your pen or crossing any edge. How did this happen? The paper has only one side!
- Outset at a different point in the Mobius strip and meet if the same thing happens.
ii

Color the edge of the strip with a highlighter. Take a highlighter and kickoff coloring the edge of the Mobius strip without lifting the highlighter from the strip. Continue with the marking until yous reach the point at which yous started. You'll find both edges are colored. This indicates that the Mobius strip has merely 1 edge!
3

Cut the Mobius strip forth the central line you lot drew earlier. With a pair of scissors, poke a hole into the centre of the Mobius strip and cut along the line until you reach the start cutting. Information technology does not, as y'all'd expect, fall autonomously into 2 separate loops; instead you at present have a single, larger ane-sided loop!^[3]
4
Cut the Mobius strip i/three of the way abroad from the edge. Like you did cutting through the center line, accept the scissors and this time, cut nearly i/3 of the way from the edge of the strip. Continue cutting until you reach the original cut.^[4]
- When you accept finished cutting, you should have one pocket-sized band and one larger band that are connected together.
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Question

When I cutting downward the eye as suggested above I get one large Mobius circle, not two interlocking ones.

Sergeantpro

Customs Respond

Cut downward the center of the Mobius strip once more and so yous volition have 2 interlocking ones.
Question

How do I cut to make three rings interconnected?

Cutting a Möbius strip downwards the center, making 2 interlocking Möbius strips. Do the same matter with one of those two; yous at present have three interlocked.
Question

Can I make a Mobius band from a sail of A4 paper? As in, no cutting or anything, simply twisting and bringing the short edges together exactly as with the long, thin rectangle?

The trouble volition exist making the required twist without tearing the paper. I think y'all'll need a sheet considerably longer and/or narrower than the A4 dimensions. A iv:1 length:width ratio is achievable, but maybe y'all'd need more than or less depending on what type of paper you utilise; stretchier materials are ameliorate than stiffer ones.