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The Elba Curves
Version 1
: Received: 24 March 2024 / Approved: 26 March 2024 / Online: 26 March 2024 (12:27:57 CET)
Version 2 : Received: 4 April 2024 / Approved: 5 April 2024 / Online: 5 April 2024 (16:27:27 CEST)
Version 2 : Received: 4 April 2024 / Approved: 5 April 2024 / Online: 5 April 2024 (16:27:27 CEST)
How to cite: Beylarov, E.B.; Hasanov, I.R. The Elba Curves. Preprints 2024, 2024031598. https://doi.org/10.20944/preprints202403.1598.v2 Beylarov, E.B.; Hasanov, I.R. The Elba Curves. Preprints 2024, 2024031598. https://doi.org/10.20944/preprints202403.1598.v2
Abstract
This article deals with special curves similar to those known in mathematics as Lamé curves. Their equations have a certain similarity with the equations of Lamé curves. But these curves are more like ellipses in appearance. Like ellipses, they have major and minor axes. These are such curves that their major and minor semi-axis coincide with an ellipse but are different than an ellipse. The main feature of these curves is that for any triangle whose base coincides with the axis of a given curve and the vertex is on a given curve, the condition an+bn=cn is obtained. The number “n” is called the degree or rank of this curve. To distinguish this group of curves, we called them Elbe curves. The equations of these lines are also provided in the paper.
Keywords
Fermat's last theorem; circle; ellipse; triangle; n-degree curves; equations
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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