<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

Published Online: Sep 26, 2019

Page range: 67 - 82

Received: Apr 01, 2018

Accepted: Jul 01, 2018

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

Keywords
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

Published Online: Sep 26, 2019

Page range: 67 - 82

Received: Apr 01, 2018

Accepted: Jul 01, 2018

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

KeywordsAlgebraic 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.

Keywords
Algebraic closed curves, elliptic curve, hexagon