Intersections of random chords of a circle
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866917988515446784 |
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| author | Bortolotto, Cynthia Souza, Victor |
| author_facet | Bortolotto, Cynthia Souza, Victor |
| contents | Where are the intersection points of diagonals of a regular $n$-gon located? What is the distribution of the intersection point of two random chords of a circle? We investigate these and related new questions in geometric probability, extend a largely forgotten result of Karamata, and elucidate its connection to the Bertrand paradox. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12866 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intersections of random chords of a circle Bortolotto, Cynthia Souza, Victor Metric Geometry Probability Where are the intersection points of diagonals of a regular $n$-gon located? What is the distribution of the intersection point of two random chords of a circle? We investigate these and related new questions in geometric probability, extend a largely forgotten result of Karamata, and elucidate its connection to the Bertrand paradox. |
| title | Intersections of random chords of a circle |
| topic | Metric Geometry Probability |
| url | https://arxiv.org/abs/2504.12866 |