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Let $J$ be a simple closed curve in $\mathbb R^{k}$ $(k\geq2)$ that isdifferentiable with non-zero derivative at a point $A_0\in J$. For a tuple ofpositive reals $a_1,\cdots,a_n$ $(n\geq3)$, each of which is less than the sumof the others, we show that there exists a polygon $Q_n$ inscribed in $J$ withsides of lengths proportional to $(a_1,\cdots,a_n)$. As a consequence, we provethe existence of triangle inscribed in $J$ similar to any given triangle.

Polygons inscribed in Jordan curves with prescribed edge ratios