Acute sets

TL;DR

This paper constructs large acute sets in high-dimensional Euclidean spaces, demonstrating sets of size at least 1.618^d and 2^{d/2}, advancing understanding of geometric configurations.

Contribution

It introduces new constructions of large acute sets in , providing explicit lower bounds on their sizes.

Findings

Constructed an acute set of size at least 1.618^d

Presented a simple example of an acute set of size at least 2^{d/2}

Enhanced understanding of geometric configurations in high dimensions

Abstract

A set of points in $\mathbb{R}^d$ is acute, if any three points from this set form an acute triangle. In this note we construct an acute set in $\mathbb{R}^d$ of size at least $1.618^d$. Also, we present a simple example of an acute set of size at least $2^{\frac{d}{2}}$.