Embedding a set of rational points in lower dimensions Original Research Article

Let Xn be a set of rational points lying on an n-dimensional flat in a Euclidean space. We prove that for n ⩾ 2, Xn is congruent to a set of rational points in R2n+1, and that for n ⩾ 3, Xn is similar to a set of rational points in R2n-1.