Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 49, No. 1, pp. 195-203 (2008)

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A projective characterization of cyclicity

Wladimir G. Boskoff and Bogdan D. Suceava

Department of Mathematics and Computer Science, University Ovidius Constanta, Romania, e-mail:, Department of Mathematics, California State University at Fullerton, Fullerton, CA, 92834--6850, U.S.A., e-mail:

Abstract: In this note we obtain a new cyclicity criterion for four points in the Euclidean plane, by using algebraic and geometric structures induced in $\mathbb{C}^2$ by the two dimensional complex projective space. We show that if four points lie on a circle in the real plane, then the type-one isotropic lines intersect $z_2$-axis in four points of real cross ratio.

Classification (MSC2000): 51N15; 51M05

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Electronic version published on: 26 Feb 2008. This page was last modified: 28 Jan 2013.

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