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.



Minimum space dimension to place n-points knowing pairwise distances
For the basic result, start with


[Wikipedia](https://en.wikipedia.org/wiki/Johnson%E2%80%93Lindenstrauss_lemma)


or Google "Johnson-Lindenstrauss Lemma".


