Geometry where direction matters -- or does it?
DOI10.1007/s00283-011-9233-4zbMath1233.52005OpenAlexW2033873183MaRDI QIDQ645313
Margarita Spirova, Horst Martini, Konrad J. Swanepoel
Publication date: 14 November 2011
Published in: The Mathematical Intelligencer (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00283-011-9233-4
Minkowski spacetriangle geometryBanach-Mazur distanceMinkowski geometryequilateral setFermat-Torricelli problemabsorbing Fermat-Torricelli configurationfinite dimensional normed spacefloating Fermat-Torricelli configurationKusner's problemReuleaux triangle
Continuous location (90B85) Geometry and structure of normed linear spaces (46B20) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Research exposition (monographs, survey articles) pertaining to convex and discrete geometry (52-02) Research exposition (monographs, survey articles) pertaining to geometry (51-02)
Related Items (2)
Cites Work
- A problem of Kusner on equilateral sets
- On Miquel's theorem and inversions in normed planes
- Abschätzungen für die Anzahl der konvexen Körper, die einen konvexen Körper berühren
- On the geometry of Minkowski planes
- Embedding of \(\ell^ k_{\infty}\) in finite dimensional Banach spaces
- Two observations regarding embedding subsets of Euclidean spaces in normed spaces
- Three-dimensional antipodal and norm-equilateral sets
- On regular 4-coverings and their application for lattice coverings in normed planes
- Geometrical properties of the Fermat-Weber problem
- Minimal surfaces, crystals, shortest networks, and undergraduate research
- Geometric methods and optimization problems
- Embedding into rectilinear spaces
- Equilateral sets in \(l_p^n\)
- Antipodality properties of finite sets in Euclidean space
- The Fermat--Torricelli problem in normed planes and spaces
- Characterizations of inner product spaces
- Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms
- On a conjecture of H. Hadwiger
- The Feuerbach circle and orthocentricity in normed places
- Equilateral simplices in normed 4-space
- Strictly antipodal sets
- Excursions into combinatorial geometry
- The geometry of Minkowski spaces -- a survey. II.
- Circle configurations in strictly convex normed planes
- A lower bound for the equilateral number of normed spaces
- Equilateral Sets in Minkowski Spaces
- A Property of Minkowskian Circles
- Equilateral dimension of the rectilinear space
- Simplexes with prescribed edge lengths in Minkowski and Banach spaces
- The geometry of Minkowski spaces -- a survey. I
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