Rectangles, curves, and Klein bottles

Schwartz, Richard

doi:10.1090/bull/1755

Rectangles, curves, and Klein bottles
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Bull. Amer. Math. Soc. 59 (2022), 1-17 Request permission

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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