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-> minimum dimension of space" does exist.
Thank you for your comments.