A Mobius strip is a geometric shape that has one surface and one boundary component. It is an important discovery in the field of geometry, analogous to the circle in which one can start at the beginning and continue to the end in an unbroken line. This intriguing ability has led to many uses of the concept and provides a look into the new possibilities and higher dimensions. The Mobius strip concept has inspired ideas for art, music, architecture and industry.
Origin of the Mobius Strip
The Mobius strip, also called the Mobius band, was discovered by August Ferdinand Mobius, an 19th century mathematician. Johann Benedict Listing independently discovered the strips properties and published a paper a short time before Mobius. The concept fascinated scientific minds at the time because of its mathematical simplicity and potential for practical use. One of the features of the Mobius strip is that it can run clockwise or counterclockwise, depending on the direction of the half-twist in the structure, giving it both a direction as well as dimensions.
How To Make A Mobius Strip
You can make your own Mobius strip to investigate its properties first-hand. Cut a narrow length of paper, 2 inches in width and about 15 inches long. Give the strip a half twist and glue or tape the 2 ends together. Get a pencil and place the tip in the center of the long band. Now, trace a line along the middle of the strip continuing until you meet the point where you started. You will see that the pencil line traces all along the strip on what appears to be both sides without interruption, but is in reality all one surface. If an ant were traveling this pencil line, it would continue without a break to the point where it started. This is the magic of the Mobius strip. If you cut the band with scissors down the middle, you will have not two separate bands, but only one much longer band.
Uses For Mobius Strips
Mobius strips have a number of practical applications that are used every day. For instance, conveyor belts can be engineered into the Mobius strip configuration to allow the material to wear evenly as it moves. This allows the belt to be used for a much longer period of time and reduces the cost of manufacturing. Continuous loop recording tape uses the Mobius concept to double playing time. Mobius strip use can also increase the longevity of printer ribbons and fabric. An electronic circuit element, called a Mobius resistor, uses the Mobius strip concept to cancel its own inductive reactance.
Beyond Mobius Strips
Cutting the Mobius strip further gives unexpected figures called paradromic rings, such as a Klein bottle and a torus, which can be applied to special design functions. Mathematically analyzing and using these complex, continuous shapes is known as topology, which is used in a variety of different fields of application.