mobius strip (mobius band) trick - (technically möbius, pronounced 'merbius')

Courtesy: Information was provided by Mr.C.S. Veeraragavan

This is an amazing trick, ideal for parties, social gatherings, light relief or ice-breakers at meetings, and bar-bets.

Cut a strip of paper so that its length is at least ten times that of its width - something around ten inches by one inch wide is fine.

PUZZLES

Puzzle 1: The strip clearly has two sides, yes? If you were asked to write number 1's all along one side of the strip, and number 2's all along the other side of the strip this would be possible, yes? So could I prevent you from doing this simply by joining the ends of the strip to create a ring or band shape?

Puzzle 2: the strip, (or now a band) is made of paper and if you cut or tear it in half you will have two separate halves, yes? And these two separate halves will actually be separate, so that they can be placed in two separate pockets, yes? So, again, simply by joining the ends of the strip to form a band, can I cut or tear this paper in half, with a continuous cut from a pair of scissors, or a continuous tear, so that you will not be able (unless by force of course) to separate the two halves? More incredibly, can I do this so that you don't actually have two halves at all? So that you actually still have one joined together strip?


You bet.......And here's how

SOLUTION:
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Twist the strip through 180 degrees, ie., half a whole turn, before joining the ends. For the purposes of the tricks you can join the strip with glue (in which case use a glue that sets quickly), sticky tape (a tape you can tear if you do not have scissors), or two staples (aligned lengthways, not sideways across the strip, each close to an edge, leaving a gap between them). You have now made a Möbius Strip, or Möbius Band, which amazingly now has only one side. Try it. It is not possible to colour or number or mark two different sides along the whole of the length of 'each side'. There is now only one side. Feed the band between your finger and thumb through a whole revolution and you will see that what were once two separate sides now pass underneath and touching your thumb.
Now for the cleverest part of the trick: Cut or tear the band in half along its length. You will need to tear or cut it carefully while feeding it through your fingers; you cannot cut it with one motion. You will be left not with two separate halves; not even two joined halves; you will be left with one big band.
Finally you can cut the new big band in half again - you will be left with two bands linked together.



Few Notes From History:

The Mobius Strip or Band has in fact been around for hundreds of years. According to scientific reports and writings this is the story: the Mobius strip was named after astronomer and mathematician August Ferdinand Möbius (1790-1868), who was a professor at the University of Leipzig. It seems he devised his strip in September 1858, and published his discovery in 1865. Interestingly, it seems that coincidentally and separately a German mathematician called Johann Benedict Listing (1808-1882) is said also to have made the same discovery in July 1858, which he published in 1861 while working on theories of another great mathematician, Leonhard Euler