The Möbius strip is well-known to topologists and to those fond of performing simple party tricks. By twisting a strip of paper through 180° before pasting its ends together, you can produce a hollow shape with only one surface and one edge. To convince the on-lookers that the shape has only one side, you can start drawing a line down the middle of it at any point and continue the line without lifting the pencil from the paper, until you return to your starting-point. You will then have shown that the single line has passed through what were, before the strip was pasted together, the two sides of the original strip of paper. The trick is both elementary and confusing: obvious and yet an irresolvable affront to one's sense of order and logic.

LRB 3 December 1981 | PDF Download