## Rectangles, curves, and Klein bottles

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Richard Evan Schwartz
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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 $\lambda$.## References

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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
- © Copyright 2021 American Mathematical Society
- Journal: Bull. Amer. Math. Soc.
**59**(2022), 1-17 - MSC (2020): Primary 51M04
- DOI: https://doi.org/10.1090/bull/1755
- MathSciNet review: 4340824