Polygons of unit area with vertices in sets of infinite planar measure
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911373064142848 |
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| author | Kovač, Vjekoslav Predojević, Bruno |
| author_facet | Kovač, Vjekoslav Predojević, Bruno |
| contents | Paul Erdős and R. Daniel Mauldin asked a series of questions on certain types of polygons of area $1$, the vertices of which can be found in every planar set of infinite Lebesgue measure. We address two of these questions, one on cyclic quadrilaterals and the other on convex polygons with congruent sides, with respectively positive and negative answers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11725 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polygons of unit area with vertices in sets of infinite planar measure Kovač, Vjekoslav Predojević, Bruno Classical Analysis and ODEs Combinatorics Metric Geometry 28A75 Paul Erdős and R. Daniel Mauldin asked a series of questions on certain types of polygons of area $1$, the vertices of which can be found in every planar set of infinite Lebesgue measure. We address two of these questions, one on cyclic quadrilaterals and the other on convex polygons with congruent sides, with respectively positive and negative answers. |
| title | Polygons of unit area with vertices in sets of infinite planar measure |
| topic | Classical Analysis and ODEs Combinatorics Metric Geometry 28A75 |
| url | https://arxiv.org/abs/2412.11725 |