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Every Jordan curve inscribes uncountably many rhombi

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Abstract

We prove that every Jordan curve in \(\mathbb {R}^2\) inscribes uncountably many rhombi. No regularity condition is assumed on the Jordan curve.

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The author is a graduate student in Boston College, supporte by a full tuition scholarship from the Mathematics Department.

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Acknowledgements

The author would like to thank Joshua Greene for proofreading and giving guidance on mathematical style and formatting.

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  1. Department of Mathematics, Boston College, Chestnut Hill, MA, 02467, USA

    Antony T. H. Fung

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  1. Antony T. H. Fung
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Correspondence to Antony T. H. Fung.

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Fung, A.T.H. Every Jordan curve inscribes uncountably many rhombi. Geom Dedicata 215, 421–441 (2021). https://doi.org/10.1007/s10711-021-00659-2

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  • DOI: https://doi.org/10.1007/s10711-021-00659-2

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