A trichotomy for rectangles inscribed in Jordan loops

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...

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Bibliographic Details
Published in:Geometriae dedicata 2020-10, Vol.208 (1), p.177-196
Main Author: Schwartz, Richard Evan
Format: Article
Language:English
Subjects:
Algebraic Geometry
Apexes
Aspect ratio
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Rectangles
Topology
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Summary: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.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-020-00516-8