Tangent Spheres of Tetrahedra and a Theorem of Grace

DOI10.1080/00029890.2020.1814673zbMath1454.51009OpenAlexW3113049957MaRDI QIDQ5140825

Hiroshi Maehara, Horst Martini

Publication date: 17 December 2020

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00029890.2020.1814673

zbMATH Keywords

tetrahedronGrace's theoremtangent sphere

Mathematics Subject Classification ID

Polyhedra and polytopes; regular figures, division of spaces (51M20) Elementary problems in Euclidean geometries (51M04) Convex sets in (3) dimensions (including convex surfaces) (52A15)

Related Items (2)

An analytic proof of a theorem of Grace ⋮ On double-\(k\)-systems of spheres

Cites Work

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• From line-systems to sphere-systems -- Schläfli's double six, Lie's line-sphere transformation, and Grace's theorem
• The generalized cross product and the volume of a simplex
• The birth of Lie's theory of groups
• \(N\)-dimensional variations on themes of Pythagoras, Euclid, and Archimedes
• An elementary and purely synthetic proof for the double six theorem of Schläfli
• Then-dimensional pythagorean theorem
• Two new block designs
• A configuration of lines in three dimensions
• Lie sphere geometry. With applications to submanifolds

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