Detail publikace
On elliptic curves with a closed component passing through a hexagon
Originální název
On elliptic curves with a closed component passing through a hexagon
Anglický název
On elliptic curves with a closed component passing through a hexagon
Jazyk
en
Originální abstrakt
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.
Anglický abstrakt
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.
Plný text v Digitální knihovně
BibTex
@article{BUT157202,
author="Miroslav {Kureš}",
title="On elliptic curves with a closed component passing through a hexagon",
annote="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.",
address="Ovidius University",
chapter="157202",
doi="10.2478/auom-2019-0019",
howpublished="print",
institution="Ovidius University",
number="2",
volume="27",
year="2019",
month="june",
pages="67--82",
publisher="Ovidius University",
type="journal article in Web of Science"
}