Delone sets associated with badly approximable triangles
Number Theory
2025-03-18 v4
Abstract
We construct new Delone sets associated with badly approximable numbers which are expected to have rotationally invariant diffraction. We optimize the discrepancy of corresponding tile orientations by investigating the linear equation where , , are three angles of a triangle used in the construction and , , are badly approximable. In particular, we show that there are exactly two solutions that have the smallest partial quotients by lexicographical ordering.
Cite
@article{arxiv.2412.11415,
title = {Delone sets associated with badly approximable triangles},
author = {Shigeki Akiyama and Emily R. Korfanty and Yanli Xu},
journal= {arXiv preprint arXiv:2412.11415},
year = {2025}
}