Polygons inscribed in Jordan curves with prescribed edge ratios

2022/11/10 by Xu, Yaping, Zhou, Ze · 1 citation
#30C35 (Secondary) #51M04 (Primary) #53A04 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2211.05515

Abstract

Let J be a simple closed curve in \mathbb R^k (k≥2) that is differentiable with non-zero derivative at a point A₀∈ J. For a tuple of positive reals a₁,⋯,a_n (n≥3), each of which is less than the sum of the others, we show that there exists a polygon Q_n inscribed in J with sides of lengths proportional to (a₁,⋯,a_n). As a consequence, we prove the existence of triangle inscribed in J similar to any given triangle.

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