 Translation and reflection of a Golomb ruler are considered trivial, so the smallest mark is customarily put at 0 and the next mark at the smaller of its two possible values.The Golomb ruler was named for Solomon W. Golomb and discovered independently by  and .Sophie Piccard also published early research on these sets, in 1939, stating as a theorem the claim that two Golomb rulers with the same distance set must be congruent.