论文标题
刻有约旦曲线的多边形
Polygons inscribed in Jordan curves with prescribed edge ratios
论文作者
论文摘要
让$ j $为$ \ mathbb r^{k} $ $（k \ geq2）$中的简单封闭曲线，与j $中的$ a_0 \ in non-Zero derivative可区分。对于积极元素的元组，$ a_1，\ cdots，a_n $ $（n \ geq3）$，每个$都比其他总和少，我们表明存在一个polygon $ q_n $，in $ j $ in $ j $，与$（a_1，\ cdots，a_n）$的长度为$ j $。结果，我们证明了与任何给定三角形相似的$ j $中刻有三角形的存在。
Let $J$ be a simple closed curve in $\mathbb R^{k}$ $(k\geq2)$ that is differentiable with non-zero derivative at a point $A_0\in J$. For a tuple of positive reals $a_1,\cdots,a_n$ $(n\geq3)$, 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 $(a_1,\cdots,a_n)$. As a consequence, we prove the existence of triangle inscribed in $J$ similar to any given triangle.
