The number of halving circles

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dc.creatorArdila, Federico
dc.date2004-08-25
dc.date.accessioned2026-07-07T05:11:34Z
dc.date.available2026-07-07T05:11:34Z
dc.descriptionA set S of 2n+1 points in the plane is said to be in general position if no three points of S are collinear and no four are concyclic. A circle is called halving with respect to S if it has three points of S on its circumference, n-1 points in its interior, and n-1 in its exterior. We prove the following surprising result: any set of 2n+1 points in general position in the plane has exactly n^2 halving circles.
dc.description7 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/math/0408354
dc.identifierhttp://arxiv.org/abs/math/0408354
dc.identifierAmerican Mathematical Monthly 111 (2004), 586-591
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72286
dc.subjectCombinatorics
dc.subjectMetric Geometry
dc.subject52C35; 05A15
dc.titleThe number of halving circles
dc.typetext

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