Orthocentric simplices as the true generalizations of triangles

DOI10.1007/s00283-013-9367-7zbMath1287.51011OpenAlexW2032920998MaRDI QIDQ384278

Horst Martini, Mowaffaq Hajja

Publication date: 27 November 2013

Published in: The Mathematical Intelligencer (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00283-013-9367-7

zbMATH Keywords

Euclidean spacesHilbert's third problemcoincidence of centersGergonne pointisogonic simplicesMonge pointorthocentric simplicespons asinorumpurity of corner vertex

Mathematics Subject Classification ID

Polyhedra and polytopes; regular figures, division of spaces (51M20) Elementary problems in Euclidean geometries (51M04) Research exposition (monographs, survey articles) pertaining to geometry (51-02) Real and complex geometry (51Mxx)

Related Items (7)

More characterizations of certain special families of simplices ⋮ Concurrence of tetrahedral cevians associated with triangle centers ⋮ Anothern-Dimensional Generalization of Pompeiu’s Theorem ⋮ Concurrency of the altitudes of a triangle ⋮ The sum of measures of the angles of a simplex ⋮ A characterization by optimization of the Monge point of a tetrahedron ⋮ Impurity of the corner angles in certain special families of simplices

Cites Work

• The open mouth theorem in higher dimensions
• The pons asinorum and related theorems for tetrahedra
• The Gergonne and Nagel centers of an \(n\)-dimensional simplex
• Coincidences of centers of edge-incentric, or balloon, simplices
• The century of Hilbert's third problem
• Orthocentric simplices and biregularity
• The Pons asinorum for tetrahedra
• Four icosahedra can meet at a point
• The orthocentric simplex as an extreme simplex
• Napoleon's theorem with weights in \(n\)-space
• The Gergonne point generalized through convex coordinates
• Triangle centers as functions
• The Gergonne and Nagel centers of a tetrahedron
• The open mouth theorem, or the scissors lemma, for orthocentric tetrahedra
• New extensions of Napoleon's theorem to higher dimensions
• Coincidences of simplex centers and related facial structures
• Orthocentric simplices and their centers
• A Vector Proof of a Theorem of Bang
• Geometry by Its History
• The Pons Asinorum in higher dimensions
• Triangle centres: some questions in Euclidean geometry
• On Nonobtuse Simplicial Partitions
• Which Tetrahedra Fill Space?
• On the Fermat-Torricelli Points of Tetrahedra and of Higher Dimensional Simplexes
• Gaspard Monge and the Monge Point of the Tetrahedron
• SOME PROPERTIES OF ORTHOCENTRIC SIMPLEXES
• On the Steiner Minimizing Point and the Corresponding Algebraic System
• The Orthocentric Simplex in Space of Three and Higher Dimensions
• Mysteries in Packing Regular Tetrahedra
• On the Measure of Solid Angles
• On the feuerbach-spheres of an orthocentric simplex
• Das BUCH der Beweise
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Orthocentric simplices as the true generalizations of triangles