Inscribed triangles of Jordan curves in $\mathbb{R}^{n}$

Aryaman Gupta; Simon Rubinstein-Salzedo

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arXiv · 2102.03953

Inscribed triangles of Jordan curves in $\mathbb{R}^{n}$

Aryaman Gupta·Simon Rubinstein-Salzedo

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Abstract

Nielsen's theorem states that any triangle can be inscribed in a planar Jordan curve. We prove a generalisation of this theorem, extending to any Jordan curve $J$ embedded in $\mathbb{R}^{n}$, for a restricted set of triangles. We then conclude by investigating a condition under which a given point of $J$ inscribes an equilateral triangle in particular.

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BibTeX RIS

Aryaman Gupta, Simon Rubinstein-Salzedo. 2021-02-08. Inscribed triangles of Jordan curves in $\mathbb{R}^{n}$. https://arxiv.org/abs/2102.03953

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