a. Let α(s), s ∈[0, l], be a plane simple closed curve. Assume that the curvature k(s) satisfies 0<k(s) ≤c, where c is a constant (thus, αis less curved than a circle of radius 1 / c ). Prove that length of α≥(2 π)/(c) b. In part a replace the assumption of being simple by " αhas rotation index N . " Prove that length of α≥(2 πN)/(c) | Numerade
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