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arXiv · 1709.03411

Acute sets of exponentially optimal size

Balázs Gerencsér·Viktor Harangi
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Abstract

We present a simple construction of an acute set of size $2^{d-1}+1$ in $\mathbb{R}^d$ for any dimension $d$. That is, we explicitly give $2^{d-1}+1$ points in the $d$-dimensional Euclidean space with the property that any three points form an acute triangle. It is known that the maximal number of such points is less than $2^d$. Our result significantly improves upon a recent construction, due to Dmitriy Zakharov, with size of order $\varphi^d$ where $\varphi = (1+\sqrt{5})/2 \approx 1.618$ is the golden ratio.

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Balázs Gerencsér, Viktor Harangi. 2017-09-11. Acute sets of exponentially optimal size. https://arxiv.org/abs/1709.03411

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