1 9 3 6 . ▁ ▁In ▁ 1 9 3 9 ▁she ▁published ▁the ▁book ▁Sur ▁les ▁ens emb les ▁de ▁distances ▁des ▁ens emb les ▁de ▁points ▁d ' un ▁es pace ▁E uclidean ▁( M ém oires ▁de ▁L ’ Univers ité ▁de ▁Ne uch ât el ▁ 1 3 , ▁ ▁Paris , ▁France : ▁Lib ra ire ▁G auth ier - V ill ars ▁and ▁C ie ., ▁ 1 9 3 9 ). ▁Its ▁subject ▁was ▁the ▁sets ▁of ▁distances ▁that ▁a ▁collection ▁of ▁points ▁in ▁a ▁E uclidean ▁space ▁might ▁determine . ▁This ▁book ▁included ▁early ▁research ▁on ▁Gol omb ▁r ul ers , ▁finite ▁sets ▁of ▁integer ▁points ▁in ▁a ▁one - dimensional ▁space ▁with ▁the ▁property ▁that ▁their ▁distances ▁are ▁all ▁distinct . ▁She ▁published ▁a ▁theorem ▁claim ing ▁that ▁every ▁two ▁Gol omb ▁r ul ers ▁with ▁the ▁same ▁distance ▁set ▁must ▁be ▁con gru ent ▁to ▁each ▁other ; ▁this ▁turned ▁out ▁to ▁be ▁false ▁for ▁certain ▁sets ▁of ▁six ▁points , ▁but ▁true ▁otherwise . ▁ ▁References ▁ ▁Further ▁reading ▁. ▁ ▁Category : 1 9 0 4 ▁birth s ▁Category : 1 9 9 0 ▁death s ▁Category : 2 0 th - century ▁mathemat icians ▁Category : Univers ity ▁of ▁La us anne ▁al umn i ▁Category : Russ ian ▁mathemat icians ▁Category : Sw iss ▁mathemat icians ▁Category : Univers ity ▁of ▁Ne uch ât el ▁fac ulty ▁Category : Set ▁the or ists ▁Category : 2 0