Möbius strip

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A spherical shell has two surfaces. You could imagnine an insect trapped inside the spherical shell or crawling freely on its visible surface. It can only remain on the outer surface or the inner surface. Möbius strip is interesting, it is a one-sided surface. It can be obtained by gluing together two ends of a strip of paper after making half a twist. It would now be possible to move along one surface and end on the other surface, without crossing an edge or leaving the surface. That is an insect walking on one suface can move from out side to inside and inside to outside. If one surface of the paper were colored blue and the other yellow, this joining of ends after half a twist makes it possible to keep moving from blue to yellow without crossing an edge. If the ends of the strip of paper were joined without making this half a twist, it would be a hollow cylinderical surface. There are clearly defined inner and outer surfaces.

It would be interesting to make a Möbius strip and then cut along the middle of its width.

Cut a strip of paper.

Give it half a twist.

Join the ends.

You have a Möbius strip.

Cut along the dotted line. The result is interesting.