Abstract
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.
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Richard Evan Schwartz Supported by N.S.F. Research Grant DMS-1204471.
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Schwartz, R.E. A trichotomy for rectangles inscribed in Jordan loops. Geom Dedicata 208, 177–196 (2020). https://doi.org/10.1007/s10711-020-00516-8
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DOI: https://doi.org/10.1007/s10711-020-00516-8