Monday, January 7, 2013

Mobius Strips

A Mobius Strip is a surface obtained by sticking the ends of a band together, giving it a single twist in the process. It was discovered by German mathematician August Ferdinand Mobius and immortalised by some of the work of Dutch artist Maurits Cornelis Escher. Today, it is probably best known as the basis of the ubiquitous recycling symbol.

The shape itself and those obtained by cutting it are somewhat counter-intuitive. For example it appears only to have one surface and one side. If you trace a pencil line across the centre or edge of a Mobius Strip, you find yourself back at the position you started from.

The study of Mobius Strips and shapes like them gave rise to a new branch of mathematics called 'topology', which is concerned with the basic properties of space and connectedness. This developed from discussing questions about simple geometry to the structure of the Universe itself. The shape is also often used in religious analogies when discussing the multifacetedness of God.

Incidentally, I often wondered why those Heath Robinson-style contraptions (which usually seem to be attached to tractors on farms) use a belt twisted into a Mobius shape. Its obvious to me now that by doing so you double the surface area of the belt in contact with the machinery and therefore prolong its life.

The youtube clip below shows some nice bamboozling tricks you can play by creating Mobius Strips in paper and then cutting them up:

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