On a necessary and sufficient cyclicity condition for a quadrilateral

2004/10/08 by Sergey Sadov, Sadov, Sergey · 1 citation
Mathematics · #13P99 #51K99 #Commutative Algebra (math.AC) #FOS: Mathematics #General Mathematics (math.GM) #Metric Geometry (math.MG) #math.AC #math.GM #math.MG #msc:13P99 #msc:51K99

paper · pdf · doi:10.48550/arxiv.math/0410234

28 pp, 2 figures, A4 paper, in Russian

arxiv created 2004/10/08 · arxiv updated 2009/12/01

Abstract

A convex quadrilateral with sides a,b,c,d, and diagonals p,q is cyclic iff abp-bcq+cdp-daq=0. This condition, in spite of its simplicity, appears to be unnoted and unexpectedly proof-resilient. We employ advanced methods of computer algebra and nonlinear analysis.

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