Acute sets of exponentially optimal size

Gerencsér, Balázs and Harangi, Viktor (2018) Acute sets of exponentially optimal size. DISCRETE AND COMPUTATIONAL GEOMETRY. pp. 1-6. ISSN 0179-5376

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Abstract

We present a simple construction of an acute set of size 2d−1+1 in Rd for any dimension d. That is, we explicitly give 2d−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 2d. Our result significantly improves upon a recent construction, due to Dmitriy Zakharov, with size of order φd where φ=(1+5–√)/2≈1.618 is the golden ratio.

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