We prove a general structural theorem about rectangles inscribed in Jordan loops. One corollary is that all but at most 4 points of any Jordan loop are vertices of inscribed rectangles. Another corollary is that a Jordan loop has an inscribed rectangle of every aspect ratio provided it has 3 points which are not vertices of inscribed rectangles.

中文翻译：

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内接于 Jordan 环的矩形的三分法

我们证明了关于内接在 Jordan 环中的矩形的一般结构定理。一个推论是，任何乔丹环的除最多 4 个点之外的所有点都是内接矩形的顶点。另一个推论是 Jordan 环具有每个纵横比的内接矩形，前提是它有 3 个不是内接矩形顶点的点。