Circumscribed Circles in Integer Geometry
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910729647423488 |
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| author | Karpenkov, Oleg Pratoussevitch, Anna Sheppard, Rebecca |
| author_facet | Karpenkov, Oleg Pratoussevitch, Anna Sheppard, Rebecca |
| contents | Integer geometry on a plane deals with objects whose vertices are points in $\mathbb Z^2$. The congruence relation is provided by all affine transformations preserving the lattice $\mathbb Z^2$. In this paper we study circumscribed circles in integer geometry. We introduce the notions of integer and rational circumscribed circles of integer sets. We determine the conditions for a finite integer set to admit an integer circumscribed circle and describe the spectra of radii for integer and rational circumscribed circles. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_04662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Circumscribed Circles in Integer Geometry Karpenkov, Oleg Pratoussevitch, Anna Sheppard, Rebecca Number Theory 52B20, 11H06, 11P21 Integer geometry on a plane deals with objects whose vertices are points in $\mathbb Z^2$. The congruence relation is provided by all affine transformations preserving the lattice $\mathbb Z^2$. In this paper we study circumscribed circles in integer geometry. We introduce the notions of integer and rational circumscribed circles of integer sets. We determine the conditions for a finite integer set to admit an integer circumscribed circle and describe the spectra of radii for integer and rational circumscribed circles. |
| title | Circumscribed Circles in Integer Geometry |
| topic | Number Theory 52B20, 11H06, 11P21 |
| url | https://arxiv.org/abs/2412.04662 |