Concurrence of tetrahedral cevians associated with triangle centers

DOI10.1007/s00022-019-0513-zzbMath1442.52008OpenAlexW3000322427WikidataQ126349758 ScholiaQ126349758MaRDI QIDQ2175728

Mostafa Hayajneh, Horst Martini, Mowaffaq Hajja, Ismail Hammoudeh

Publication date: 30 April 2020

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00022-019-0513-z

zbMATH Keywords

circumcenterincentercentroidorthocenterorthocentric simplexcircumscriptible simplexisodynamic simplexisogonic simplexGergonne centerNagel centercevianFermat- Torricelli pointLemoine center

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Three-dimensional polytopes (52B10) Polyhedra and polytopes; regular figures, division of spaces (51M20) Euclidean analytic geometry (51N20) Symmetry properties of polytopes (52B15)

Cites Work

• Orthocentric simplices as the true generalizations of triangles
• Remarks on the circumcenter of mass
• The Gergonne and Nagel centers of an \(n\)-dimensional simplex
• Coincidences of centers of edge-incentric, or balloon, simplices
• Geometric methods and optimization problems
• Triangle centers as functions
• The Gergonne and Nagel centers of a tetrahedron
• Pre-kites: simplices having a regular facet
• A concept of the mass center of a system of material points in the constant curvature spaces
• Kites as the only doubly special simplices
• Concurrency of the altitudes of a triangle
• Orthocentric simplices and their centers
• More characterizations of certain special families of simplices
• Triangle centres: some questions in Euclidean geometry
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