Geometric constructions on cycles in \(\mathbb{R}^n\)

DOI10.1216/RMJ-2015-45-5-1709zbMath1343.51014arXiv1311.5656MaRDI QIDQ908268

Borut Jurčič Zlobec, Neža Mramor Kosta

Publication date: 4 February 2016

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.5656

zbMATH Keywords

cyclesprojectiondeterminantLie sphere geometryprojective subspaceLie form

Mathematics Subject Classification ID

Elementary problems in Euclidean geometries (51M04) Geometric constructions in real or complex geometry (51M15) Quadratic and bilinear forms, inner products (15A63)

Cites Work

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• Apollonius tenth problem via radius adjustment and Möbius transformations
• The Apollonius contact problem and Lie contact geometry
• The law of sines for tetrahedra and \(n\)-simplices
• Geometric constructions on cycles
• Planar sections of the quadric of Lie cycles and their Euclidean interpretations
• Lie sphere geometry. With applications to submanifolds
• Configurations of cycles and the Apollonius problem

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