Because both objects have just one hole, one can be deformed into the other through just stretching and bending. The number of holes in an object is a property which can be changed only through cutting or gluing.
Imagine writing yourself a note on a see-through surface, then taking a walk around on that surface. The surface is orientable if, when you come back from your walk, you can always read the note.
On a nonorientable surface, you may come back from your walk only to find that the words you wrote have apparently turned into their mirror image and can be read only from right to left. On the two-sided loop, the note will always read from left to right, no matter where your journey took you. When the GIF starts, the dots listed off clockwise are black, blue and red.
This transformation is impossible on an orientable surface like the two-sided loop. The concept of orientability has important implications. Next we bend the cylinder and then glue together the ends so that the arrows agree. We cannot realize this figure in three dimensions.
We can pretend that we pass the end of the cylinder through itself before gluing the ends together, but mathematicians often prefer to think of this object as existing in 4-dimensional space.
Just like the Mobius stip, the Klein Bottle is a one-sided figure. Unlike the Mobius Strip, the Klein bottle does not have any boundary though. The Klein Bottle has no holes or punctures. We would say that the surface is closed. Take a second strip of paper and curve it round into a loop, but before gluing the ends together, twist one end of the paper, to make a loop with a single twist in it. Try making one with two twists in it — does that make any difference?
This creates a loop of paper with only one surface and one edge. When a strip has an even number of twists in it, this connects the top surface of one end with the top surface of the other, and so creates a loop with two surfaces. Test by drawing a line down the centre. This creates a one larger loop with two twists.
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