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 Mï¿½bius (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.
Dan Summons, Theory Physics Undergrad Student, UOS, Souhampton
'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'