The Maximum of the Volume of a Cevian Simplex and its Parts

[2507.10067] The Maximum of the Volume of a Cevian Simplex and its Parts Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Metric Geometry arXiv:2507.10067 (math) [Submitted on 14 Jul 2025 ( v1 ), last revised 11 Apr 2026 (this version, v2)] Title: The Maximum of the Volume of a Cevian Simplex and its Parts Authors: Yagub N. Aliyev View a PDF of the paper titled The Maximum of the Volume of a Cevian Simplex and its Parts, by Yagub N. Aliyev View PDF HTML (experimental) Abstract: The cevian triangle corresponding to an interior point $M$ of a triangle is the triangle determined by the feet of the three cevians concurrent at $M$. It is known that the area of the cevian triangle for an interior point $M$ of a triangle is at most $\frac{1}{4}$ of the area of the triangle, with maximum attained when $M$ is the triangle's centroid. This can be generalized from triangles to $n$-dimensional simplices, with $\frac{1}{4}$ replaced by $\frac{1}{n^n}$, using barycentric coordinates. We also use this method to solve two optimization problems about the parts of this simplex. Subjects: Metric Geometry (math.MG) MSC classes: 51M04, 51M05, 51M16, 51M25 Cite as: arXiv:2507.10067 [math.MG] (or arXiv:2507.10067v2 [math.MG] for this version) https://doi.org/10.48550/arXiv.2507.10067 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yagub Aliyev [ view email ] [v1] Mon, 14 Jul 2025 08:52:31 UTC (4 KB) [v2] Sat, 11 Apr 2026 14:59:49 UTC (5 KB) Full-text links: Access Paper: View a PDF of the paper titled The Maximum of the Volume of a Cevian Simplex and its Parts, by Yagub N. Aliyev View PDF HTML (experimental) TeX Source view license Current browse context: math.MG < prev | next > new | recent | 2025-07 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

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