Trie absolute curvature of a smooth curve with parametrization (Ï, I) at a point x0 = Ï(t0)

Trie absolute curvature of a smooth curve with parametrization (ψ, I) at a point x0 = ψ(t0) is the number

when this limit exists, where 0(t) is the angle between ψ'(t) and ψ'(t0), and (t) is the arc length of if ψ(I) from ψ(t) to ψ(t0). [Thus K measures how rapidly θ (t) changes with respect to arc length.]
a) Given a, b ˆˆ Rn, b ‰  0, prove that the absolute curvature of the line A from a to b is zero at each point x0 on A.
b) Prove that the absolute curvature of the circle of radius r is 1 /r at each point x0 on C.

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9 (t)