Publication detail

On elliptic curves with a closed component passing through a hexagon

KUREŠ, M.

Original Title

On elliptic curves with a closed component passing through a hexagon

English Title

On elliptic curves with a closed component passing through a hexagon

Type

journal article in Web of Science

Language

en

Original Abstract

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.

English abstract

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.

Keywords

algebraic closed curves, elliptic curve, hexagon

Released

01.06.2019

Publisher

Ovidius University

Location

Constanta

Pages from

67

Pages to

82

Pages count

16

URL

Full text in the Digital Library

Documents

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"
}