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I laughed at the second one. The first one is apparently over my head.
To make it simple, a moibus band is a one sided, never ending strip. It's one sided because you take a strip, twist it, then join the ends. It seems like it should still have two sides, but if you take a pencil and draw a line down it, you will get back to the original point without ever taking the pencil off the strip. It's pretty cool.