The open mouth theorem, or the scissors lemma, for orthocentric tetrahedra

DOI10.1007/s00022-012-0116-4zbMath1261.51015OpenAlexW2006077920WikidataQ61534690 ScholiaQ61534690MaRDI QIDQ1928608

Sadi Abu-Saymeh, Mostafa Hayajneh, Mowaffaq Hajja

Publication date: 3 January 2013

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

Full work available at URL: https://doi.org/10.1007/s00022-012-0116-4

zbMATH Keywords

solid angletrihedral angleopen mouth theorempolar sinecontent of a solid angleorthocentric tetrahedronsine of a solid angle

Mathematics Subject Classification ID

Polyhedra and polytopes; regular figures, division of spaces (51M20) Elementary problems in Euclidean geometries (51M04)

Related Items (7)

Irreducibility of the Cayley-Menger determinant and of a class of related polynomials ⋮ Orthocentric simplices as the true generalizations of triangles ⋮ Lack of relative monotonicity among various measures of trihedral angles ⋮ The open mouth theorem in higher dimensions ⋮ The sum of measures of the angles of a simplex ⋮ Impurity of the corner angles in certain special families of simplices ⋮ Newton Quadrilaterals, the Associated Cubic Equations, and Their Rational Solutions

Cites Work

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• The open mouth theorem in higher dimensions
• Orthocentric simplices and biregularity
• The Pons asinorum for tetrahedra
• The law of sines for tetrahedra and \(n\)-simplices
• Lack of relative monotonicity among various measures of trihedral angles
• Equicevian points on the altitudes of a triangle
• Orthocentric simplices and their centers
• The Pons Asinorum in higher dimensions
• The Orthocentric Simplex in Space of Three and Higher Dimensions
• The extreme coverings of 4-space by spheres
• Vector Proofs in Solid Geometry
• On the Measure of Solid Angles
• The Sums of the Dihedral and Trihedral Angles in a Tetrahedron

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