Every highschool student recognizes a Möbius strip, and one out of two mathematical institutions has it in its logo. Indeed every science museum shows you a large model of this surface and moves a tiny vehicle along the blue median to make the visitor realize how it fails to have two sides. But if you really understand its algebra, topology, analysis and its geometry and you therefore comprehend its associative multiplication (which is continuous, differentiable and induced by the semigroup multiplication of Communicated by László Márki.