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The Mobius Strip

To make and check out a Mobius strip.
1. Take a long rectangular strip of paper (try 1 in. by 10 in.).
2. Give it a half twist (turn one end over).
3. Tape the two twisted ends together.
4. Take a pencil and draw a line along the length. How many sides does the moebius strip have?
5. Take a pair of scissors and cut the Mobius strip along the line you have drawn. What happened?
6. Cut a new Mobius strip one-third of the way in from one edge. The cut will meet itself eventually.What happened?

Because of the half twist, the Möbius Strip
has only one side and one edge!
Cut in half, the Mobius strip becomes
a single narrower double-length twisted loop.
Cut in thirds, you end up with two loops,
leaving a thinner version of itself intact,
and producing a second loop,
twice as long, with two half-twists.

A mathematician confided
That a Mobius 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.