Jordan curves inscribe a positive measure of rectangles

Joshua Evan Greene; Andrew Lobb

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arXiv · 2604.17116

Jordan curves inscribe a positive measure of rectangles

Joshua Evan Greene·Andrew Lobb

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Abstract

Suppose that $\gamma \subset \mathbb{C}$ is a Jordan curve of diameter $2R$ which encloses a region of area $A$. We prove that there exists a subset $I \subset (0,\pi)$ of measure at least $A/R^2$ such that if $\theta \in I$, then there exist four points on $\gamma$ at the vertices of a rectangle whose diagonals meet at angle $\theta$.

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BibTeX RIS

Joshua Evan Greene, Andrew Lobb. 2026-04-18. Jordan curves inscribe a positive measure of rectangles. https://arxiv.org/abs/2604.17116

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