Mobius strip
- Date: 2007-06-21 - Word Count: 611
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Otherwise known as the Mobius band, the Mobius strip is a surface with only one side and only one boundary component. It possesses the mathematical property of being a ruled surface, but at the same time non-orientable. Its discovery was done independently by two mathematicians, both German, in 1858. Those two mathematicians were August Ferdinand Mobius and Johann Benedict Listing.
How can you obtain this surface? The easiest method would be by taking a strip of paper, applying a half twist to it and reconnecting the ends afterwards in order to form a single strip. Depending on how you apply the half-twist, you can obtain two Mobius strips, one clockwise and the other counter-clockwise.
There are some strange properties that Mobius strips have. For instance, drawing a line on the middle of the paper strip will lead you back to the starting point. Thus, the line will cross the entire surface and the length will be double of the original strip of paper.
If the strip of paper would be cut exactly across that line, you will obtain a strip of paper with two half twist, instead of two pieces of paper with only one half twist. This happens because there is only one edge twice as long as the original strip of paper. The surface with two or more half twists can no longer be called Mobius strips, because this has only one half twist.
There are lots of other strange properties. If you were to cut the strip roughly a third of the way in from one of the edges, the result would be again unexpected. There would be a thin Mobius strip and a strip with two half twists. There are lots of strange combinations obtained from cutting Mobius strips and giving them more half twists. The figures you get are called paradromic rings.
Cutting Mobius strips is not the only way to obtain different and strange figures. Gluing the edges of two Mobius strips also gives you the chance to get some unexpected results. The figures you can obtain through this process are the Klein bottle or the real projective plane. The two are obtained by gluing two Mobius strips along different edges. The main property these figures have in common with the Mobius strip is that they all have only one surface, even if it looks like they don't.
The strange properties of Mobius strips have been a determinant factor in its popularity. From sculpture to literature, the Mobius strip has been an inspiration to a lot of works in those areas. Even in recent years, movies and video games have based some events on it. It has even reached out as means for advertising, being adopted as a logo by different companies.
An object with these mysterious properties was bound to have some theological meaning. Some consider the Mobius strip to be a symbol of the Creator, who created everything that surrounds us from himself. Some people even consider that a generalized pattern of Mobius strips can be used to describe the universe. One thing is for sure, this pattern has a lot of meaning.
If you would like to purchase jewelry shaped like a Mobius strip, you can go online and visit ka-gold-jewelry.com. On this website, lots of other jewelry can be found, with other meanings and other properties. You can be sure that all the jewelry you purchase from this website has some deep meaning.
There is great mystery attributed to the Mobius strip. Because it is a mathematical discovery, and we all know mathematics as the universal language, it is believed to be a way to describe the universe. It also serves as an inspiration to artists.
How can you obtain this surface? The easiest method would be by taking a strip of paper, applying a half twist to it and reconnecting the ends afterwards in order to form a single strip. Depending on how you apply the half-twist, you can obtain two Mobius strips, one clockwise and the other counter-clockwise.
There are some strange properties that Mobius strips have. For instance, drawing a line on the middle of the paper strip will lead you back to the starting point. Thus, the line will cross the entire surface and the length will be double of the original strip of paper.
If the strip of paper would be cut exactly across that line, you will obtain a strip of paper with two half twist, instead of two pieces of paper with only one half twist. This happens because there is only one edge twice as long as the original strip of paper. The surface with two or more half twists can no longer be called Mobius strips, because this has only one half twist.
There are lots of other strange properties. If you were to cut the strip roughly a third of the way in from one of the edges, the result would be again unexpected. There would be a thin Mobius strip and a strip with two half twists. There are lots of strange combinations obtained from cutting Mobius strips and giving them more half twists. The figures you get are called paradromic rings.
Cutting Mobius strips is not the only way to obtain different and strange figures. Gluing the edges of two Mobius strips also gives you the chance to get some unexpected results. The figures you can obtain through this process are the Klein bottle or the real projective plane. The two are obtained by gluing two Mobius strips along different edges. The main property these figures have in common with the Mobius strip is that they all have only one surface, even if it looks like they don't.
The strange properties of Mobius strips have been a determinant factor in its popularity. From sculpture to literature, the Mobius strip has been an inspiration to a lot of works in those areas. Even in recent years, movies and video games have based some events on it. It has even reached out as means for advertising, being adopted as a logo by different companies.
An object with these mysterious properties was bound to have some theological meaning. Some consider the Mobius strip to be a symbol of the Creator, who created everything that surrounds us from himself. Some people even consider that a generalized pattern of Mobius strips can be used to describe the universe. One thing is for sure, this pattern has a lot of meaning.
If you would like to purchase jewelry shaped like a Mobius strip, you can go online and visit ka-gold-jewelry.com. On this website, lots of other jewelry can be found, with other meanings and other properties. You can be sure that all the jewelry you purchase from this website has some deep meaning.
There is great mystery attributed to the Mobius strip. Because it is a mathematical discovery, and we all know mathematics as the universal language, it is believed to be a way to describe the universe. It also serves as an inspiration to artists.
Related Tags: properties, mobius strip, surface, edge
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