Metric Spaces

Abstract

Consider a set of particles P _i , i = 1,..., n. To locate these particles in the space E³, we need a reference system. Let the Cartesian coordinates of Pi be (ξ _i , η _i , ζ _i ) for each i. Identifying (ξ _i , η _i , ζ _i ) with (x ₁, x ₂, x ₃), (ξ _i , η _i , ζ _i ) with (x ₄, x ₅, x ₆), and so on, we obtain a vector x of the Euclidean space ℝ³ⁿ with coordinates (x ₁, x ₂,..., x _3n ). This vector determines the positions of all particles in the set.