<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In general, there exists an ellipse passing through the vertices of a convex pentagon, but any ellipse passing through the vertices of a convex hexagon does not have to exist. 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.</p></abstract>

In general, there exists an ellipse passing through the vertices of a convex pentagon, but any ellipse passing through the vertices of a convex hexagon does not have to exist. 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.

On elliptic curves with a closed component passing through a hexagon

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On elliptic curves with a closed component passing through a hexagon"}

In general, there exists an ellipse passing through the vertices of a convex pentagon, but any ellipse passing through the vertices of a convex hexagon does...

On elliptic curves with a closed component passing through a hexagon

Pubblicato online: 26 set 2019

Pagine: 67 - 82

Ricevuto: 01 apr 2018

Accettato: 01 lug 2018

DOI: https://doi.org/10.2478/auom-2019-0019

Parole chiave
Algebraic closed curves, elliptic curve, hexagon

© 2019 Miroslav Kureš, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On elliptic curves with a closed component passing through a hexagon

Pubblicato online: 26 set 2019

Pagine: 67 - 82

Ricevuto: 01 apr 2018

Accettato: 01 lug 2018

DOI: https://doi.org/10.2478/auom-2019-0019

Parole chiaveAlgebraic closed curves, elliptic curve, hexagon

© 2019 Miroslav Kureš, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Parole chiave
Algebraic closed curves, elliptic curve, hexagon