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Gnome children love playing the Möbius Ring* game, especially on windy or rainy nights when they can't go out to play in the fields and meadows.
These rings have very special properties because of the way they are given a little half twist. If you colour the surface of an ordinary paper ring, it will be coloured on the outside only. The inside will remain white. It is therefore a normal ring with two surfaces. But a Möbius ring is very different. If you start to colour one of the surfaces of a Möbius ring without taking your hand away, you will end up by colouring both sides. So the ring only has one surface!
Making a Möbius ring is very easy. First cut out a strip of paper 5cm wide and 50cm long. Then take one of the ends and twist it once in the middle. Carefully glue the two ends together. You can now continue with the experiment.
Use a pair of scissors to cut the strip of paper in half lengthways.
What will the result be?
You will have just one ring double the length of the first one.
For the next experiment, make another Möbius ring and cut it one third in from the outer edge of the paper. What will the result be? You will have two rings linked together; one of these is the Möbius ring and the other is a normal paper ring, twice as long as the original.
That is what these two gnome children have discovered.
* August Ferdinand Möbius, a German mathematician, was born in 1790. He became famous in the world of science for discovering a circle with only one side. But was Möbius really the inventor of the ring which bears his name? Even The Secret Book does not give us the answer to this mystery. Did the gnomes learn about it from him, I wonder? Or did Möbius only find out about the ring after a secret encounter he had with one of our ancestors?
These rings have very special properties because of the way they are given a little half twist. If you colour the surface of an ordinary paper ring, it will be coloured on the outside only. The inside will remain white. It is therefore a normal ring with two surfaces. But a Möbius ring is very different. If you start to colour one of the surfaces of a Möbius ring without taking your hand away, you will end up by colouring both sides. So the ring only has one surface!
Making a Möbius ring is very easy. First cut out a strip of paper 5cm wide and 50cm long. Then take one of the ends and twist it once in the middle. Carefully glue the two ends together. You can now continue with the experiment.
Use a pair of scissors to cut the strip of paper in half lengthways.
What will the result be?
You will have just one ring double the length of the first one.
For the next experiment, make another Möbius ring and cut it one third in from the outer edge of the paper. What will the result be? You will have two rings linked together; one of these is the Möbius ring and the other is a normal paper ring, twice as long as the original.
That is what these two gnome children have discovered.
* August Ferdinand Möbius, a German mathematician, was born in 1790. He became famous in the world of science for discovering a circle with only one side. But was Möbius really the inventor of the ring which bears his name? Even The Secret Book does not give us the answer to this mystery. Did the gnomes learn about it from him, I wonder? Or did Möbius only find out about the ring after a secret encounter he had with one of our ancestors?
