The open mouth theorem in higher dimensions

DOI10.1016/j.laa.2012.03.012zbMath1244.51004OpenAlexW2012812274WikidataQ61534654 ScholiaQ61534654MaRDI QIDQ426100

Mowaffaq Hajja, Mostafa Hayajneh

Publication date: 11 June 2012

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2012.03.012

zbMATH Keywords

simplexpositive definite matrixGram matrixfacetGram determinantpons asinorumprincipal minoracute polyhedral angleacute simplexbridge of assescontent of a polyhedral angleDe Gua's theoremgeneralized Pythagoras theoremHinge theoremobtuse polyhedral angleobtuse simplexopen mouth theoremorthocentric simplexpolar sine of a polyhedral anglepolyhedral anglerectangular polyhedral anglerectangular simplexscissors lemmasine of a polyhedral angle

Mathematics Subject Classification ID

Elementary problems in Euclidean geometries (51M04)

Related Items (7)

Orthocentric simplices as the true generalizations of triangles ⋮ Lack of relative monotonicity among various measures of trihedral angles ⋮ The open mouth theorem, or the scissors lemma, for orthocentric tetrahedra ⋮ Pre-kites: simplices having a regular facet ⋮ The sum of measures of the angles of a simplex ⋮ Impurity of the corner angles in certain special families of simplices ⋮ The pons asinorum and related theorems for tetrahedra

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Coincidences of centers of edge-incentric, or balloon, simplices
• The Pons asinorum for tetrahedra
• The law of sines for tetrahedra and \(n\)-simplices
• Napoleon's theorem with weights in \(n\)-space
• The generalized sine theorem and inequalities for simplices
• 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
• The Pons Asinorum in higher dimensions
• Then-dimensional pythagorean theorem
• On the Problem of Runs
• The Orthocentric Simplex in Space of Three and Higher Dimensions
• History of Mathematics
• On the Measure of Solid Angles
• Letter to the editor

This page was built for publication: The open mouth theorem in higher dimensions