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