Let us consider a standard braid diagram as a three-dimensional figure viewed from the top; what happens when we look at this figure from the side? Then we can obtain a new braid, and studying the connection between the initial braid and the derived braid so obtained provides both a new simple proof for the existence of the right greedy normal form of positive braids and a geometrical interpretation for the automatic structure of the braid groups. AMS Subject classification: 20F36, 57M25