ABSTRACT
A curve ϕ : I → Rn is said to be of class Cr if ϕ is Cr on an open interval containing I. A C1 curve ϕ is smooth if ϕ′(t) 6= 0 for all t ∈ I. For example, on [−1, 1] the curve ϕ(t) = (t, t2) is smooth but the curve ψ(t) = (t3, t6), which has the same trace as ϕ, is not.
