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Miklós Schweitzer 2012 P7

Source: Miklós Schweitzer 2012 P7

August 20, 2018
college contestsMiklos Schweitzerprobabilityreal analysis

Problem Statement

Let Γ\Gamma be a simple curve, lying inside a circle of radius rr, rectifiable and of length ℓ\ell. Prove that if ℓ>krπ\ell > kr\pi, then there exists a circle of radius rr which intersects Γ\Gamma in at least k+1k+1 distinct points.
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