Delone sets associated with badly approximable triangles
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929761064845312 |
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| author | Akiyama, Shigeki Korfanty, Emily R. Xu, Yanli |
| author_facet | Akiyama, Shigeki Korfanty, Emily R. Xu, Yanli |
| contents | 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 $x+y+z=1$ where $πx$, $πy$, $πz$ are three angles of a triangle used in the construction and $x$, $y$, $z$ are badly approximable. In particular, we show that there are exactly two solutions that have the smallest partial quotients by lexicographical ordering. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11415 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Delone sets associated with badly approximable triangles Akiyama, Shigeki Korfanty, Emily R. Xu, Yanli Number Theory 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 $x+y+z=1$ where $πx$, $πy$, $πz$ are three angles of a triangle used in the construction and $x$, $y$, $z$ are badly approximable. In particular, we show that there are exactly two solutions that have the smallest partial quotients by lexicographical ordering. |
| title | Delone sets associated with badly approximable triangles |
| topic | Number Theory |
| url | https://arxiv.org/abs/2412.11415 |