A Cubic Curve Associated to a Menelaus-Ceva Triple

This note aims to study the cubic curve naturally associated to a triple of strictly positive numbers satisfying the Menelaus-Ceva condition. Restricting to a fixed triangle $\Delta $ we discuss several main points and the Lemoine line of $\Delta $ in this unified framework and we point out the cases when the cubic curve is an elliptic one.

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Publication Details

Journal
International Electronic Journal of Geometry
Published
2026-04-22
DOI
https://doi.org/10.36890/iejg.1803403
Primary Topic
Mathematics and Applications
Type
article
Field-Weighted Citation Impact
0.00
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article

A Cubic Curve Associated to a Menelaus-Ceva Triple

Mircea Crâşmăreanu
International Electronic Journal of Geometry
Mathematics and Applications
article

A Cubic Curve Associated to a Menelaus-Ceva Triple

Mircea Crâşmăreanu
article en

Abstract

This note aims to study the cubic curve naturally associated to a triple of strictly positive numbers satisfying the Menelaus-Ceva condition. Restricting to a fixed triangle $\Delta $ we discuss several main points and the Lemoine line of $\Delta $ in this unified framework and we point out the cases when the cubic curve is an elliptic one.

International Electronic Journal of GeometryVol. 19(1)
Alexandru Ioan Cuza University (RO)
Reduced inequalities
Openalex Percentile: Top 7%
Mathematics and Applications
DOIOpen Access PDFOpenAlex
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