On elliptic curves with a closed component passing through a hexagon
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In general, there exists an ellipse passing through the vertices of a convex pentagon, but there is no ellipse passing through the vertices of a convex hexagon. Thus, attention is turned to algebraic curves of the third degree, namely to the closed component of certain elliptic curves. This closed curve will be called the spekboom curve. Results of numerical experiments and some hypotheses regarding hexagons of special shape connected with the existence of this curve passing through the vertices are presented and suggested. Some properties of the spekboom curve are described, too.
Keywordsalgebraic closed curves, elliptic curve, hexagon
Document typePeer reviewed
Document versionFinal PDF
SourceAnalele Stiintifice Ale Universitatii Ovidius Constanta, Seria Matematica. 2019, vol. 27, issue 2, p. 67-82.
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