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Bulletin of the American Mathematical Society

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Rectangles, curves, and Klein bottles


Author: Richard Evan Schwartz
Journal: Bull. Amer. Math. Soc. 59 (2022), 1-17
MSC (2020): Primary 51M04
DOI: https://doi.org/10.1090/bull/1755
Published electronically: September 13, 2021
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Abstract: In this article I will survey some results about inscribing triangles and quadrilaterals in Jordan curves. I will focus on the recent result of Josh Greene and Andrew Lobb, which says that for any smooth embedded loop $C$ and any aspect ratio $\lambda$, there are four points in $C$ which make the vertices of a rectangle of aspect ratio $\lambda$.


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Additional Information

Richard Evan Schwartz
Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island
MR Author ID: 605575

Received by editor(s): April 20, 2021
Published electronically: September 13, 2021
Additional Notes: Supported by N.S.F. Research Grant DMS-1204471
Article copyright: © Copyright 2021 American Mathematical Society