Abstract: | For each irrational number , with continued fraction expansion , we classify, up to translation, the one dimensional almost periodic tilings which can be constructed by the projection method starting with a line of slope . The invariant is a sequence of integers in the space and whenever modulo the equivalence relation generated by tail equivalence and . Each tile in a tiling , of slope , is coded by an integer . Using a composition operation, we produce a sequence of tilings . Each tile in gets absorbed into a tile in . A choice of a starting tile in will thus produce a sequence in . This is the invariant. |