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Let us consider two closed curves M, N of class C 1 and two functions ϕ : M → IR, ψ : N → IR of class C 1 , called measuring functions. The natural pseudo-distance d between the pairs (M, ϕ), (N , ψ) is defined as the infimum of Θ(f ) def = max P ∈M |ϕ(P ) − ψ(f (P ))|, as f varies in the set of all homeomorphisms from M onto N . The problem of finding the possible values for d naturally arises. In this paper we prove that under appropriate hypotheses the natural pseudo-distance equals eitherdoi:10.1515/forum.2009.049 fatcat:irgzhqp2szfyjg3gaqooxfm3h4