On the minimal area of quadrangles circumscribed about planar convex bodies

[2506.05185] On the minimal area of quadrangles circumscribed about planar convex bodies Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Metric Geometry arXiv:2506.05185 (math) [Submitted on 5 Jun 2025] Title: On the minimal area of quadrangles circumscribed about planar convex bodies Authors: Ferenc Fodor , Florian Grundbacher View a PDF of the paper titled On the minimal area of quadrangles circumscribed about planar convex bodies, by Ferenc Fodor and Florian Grundbacher View PDF HTML (experimental) Abstract: We show that every planar convex body is contained in a quadrangle whose area is less than $(1 - 2.6 \cdot 10^{-7}) \sqrt{2}$ times the area of the original convex body, improving the best known upper bound by W. Kuperberg. Comments: 11 pages, 3 figures Subjects: Metric Geometry (math.MG) MSC classes: 52A27 (Primary) 52A10, 52A40 (Secondary) Cite as: arXiv:2506.05185 [math.MG] (or arXiv:2506.05185v1 [math.MG] for this version) https://doi.org/10.48550/arXiv.2506.05185 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Discrete Math 349, No. 7, (2026), 115087 Related DOI : https://doi.org/10.1016/j.disc.2026.115087 Focus to learn more DOI(s) linking to related resources Submission history From: Florian Grundbacher [ view email ] [v1] Thu, 5 Jun 2025 15:57:49 UTC (13 KB) Full-text links: Access Paper: View a PDF of the paper titled On the minimal area of quadrangles circumscribed about planar convex bodies, by Ferenc Fodor and Florian Grundbacher View PDF HTML (experimental) TeX Source view license Current browse context: math.MG < prev | next > new | recent | 2025-06 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Minimal-Volume Equiangular Hyperbolic $4$-Polytopes#927558
• Perimeter approximation of convex discs in the hyperbolic plane and on the sphere#131166
• Parallelepipeds of maximal facet area and total edge length in ellipsoids, through prescribed boundary points#1104898
• The Probability That the Incenter of a Triangle Lies in a Random Diameter Disk#780808
• The Probability That the Incenter of a Triangle Lies in a Random Diameter Disk#779433