{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-equilateral-small-octagon-of-maximal","title":"The equilateral small octagon of maximal width","arxiv_id":"2110.00036","date":"2021-09-30","proceeding":null,"authors":["Christian Bingane","Charles Audet"],"abstract":"A small polygon is a polygon of unit diameter. The maximal width of an equilateral small polygon with $n=2^s$ vertices is not known when $s \\ge 3$. This paper solves the first open case and finds the optimal equilateral small octagon. Its width is approximately $3.24\\%$ larger than the width of the regular octagon: $\\cos(\\pi/8)$. In addition, the paper proposes a family of equilateral small $n$-gons, for $n=2^s$ with $s\\ge 4$, whose widths are within $O(1/n^4)$ of the maximal width.","url_abs":"https://arxiv.org/abs/2110.00036v2","url_pdf":"https://arxiv.org/pdf/2110.00036v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"the-equilateral-small-octagon-of-maximal","repo_url":"https://github.com/cbingane/optigon","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}