Let $P$ be a set of $n$ points. Assuming I know the pairwise distances for each pair of points. What would be the minimum dimension of the space in which I could place those $n$ points with respect to the different pairwise distances.
The idea would be to set a first point at random coordinates in a multi-dimensional space. Then, add the other $n-1$ points so that the pairwise distances are respected.
Sorry, it's maybe a trivial question for mathematicians but I'm still wondering if the relation: "number of points $\to$ minimum dimension of space" does exist.