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.",