On sets defining few ordinary circles

DOI10.1007/s00454-017-9885-8zbMath1384.52023arXiv1607.06597OpenAlexW2506035431WikidataQ47147715 ScholiaQ47147715MaRDI QIDQ1702346

Josef Schicho, Hossein Nassajian Mojarrad, Aaron Lin, Konrad J. Swanepoel, Mehdi Makhul, Frank de Zeeuw

Publication date: 28 February 2018

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.06597

zbMATH Keywords

inversionSylvester-Gallaicircular curvesGreen-Taoordinary circles

Mathematics Subject Classification ID

Plane and space curves (14H50) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Erd?s problems and related topics of discrete geometry (52C10)

Related Items

The Elekes-Szabó theorem in four dimensions, Ordinary hyperspheres and spherical curves, On the minimum number of ordinary conics, On sets defining few ordinary planes, On sets defining few ordinary hyperplanes, On sets defining few ordinary solids, Ordinary planes, coplanar quadruples, and space quartics

Cites Work

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• On sets defining few ordinary lines
• Polynomials vanishing on Cartesian products: the Elekes-Szabó theorem revisited
• On the Sylvester-Gallai theorem for conics
• On the number of ordinary circles determined by \(n\) points
• On sets defining few ordinary planes
• Problems in geometry. Transl. from the French by Silvio Levy
• A Sylvester theorem for conic sections
• On the number of circles determined by \(n\) points in the Euclidean plane
• A generalisation of Sylvester's problem to higher dimensions
• On the Number of Ordinary Conics
• Research Problems in Discrete Geometry
• The Arithmetic of Elliptic Curves
• Cayley-Bacharach theorems and conjectures
• On the number of circles determined byn points
• The Lines and Planes Connecting the Points of a Finite Set