What is the Mobius Strip?

Asked by: Kartikeya Shah

Answer

Very roughly a surface is orientable if it has two sides so that, for example, is it possible to paint it with two different colours. A sheet of paper or the surface of a sphere are examples of orientable surfaces. A Mobius strip is a non-orientable surface: you can build one with a strip of paper (twist the strip and glue end together to form a ring) and verify that it has only one side: it is not possible to paint it with two colours.



In short a Mobius strip only has one side and one edge.

Ants would be able to walk on the Mobius strip on a single surface indefinitely since there is no edge in the direction of their movement. Just like what M.C. Escher depicted in his famous picture (shown on the right.)

Mobius strip was named after the astronomer and mathematician August Ferdinand M'bius (1790-1868). He came up with his 'strip' in September 1858. Independently, German mathematician Johann Benedict Listing (1808-1882) devised the same object in July 1858. Perhaps we should be talking about the Listing strip instead of the Mobius strip.

To learn more about the Mobius strip go to: ScienceNews MathTrek
Learn more about the Mobius strip at Fermilab.

You can buy Escher's 'Ants' poster by clicking here.

Answered by: Dan Summons, Theory Physics Undergrad Student, UOS, Souhampton