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Cubics, hyperbolas and steiner ellipses

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Abstract

In this article, we will show that for every choice of real numbers \(a_1\) and \(a_2\), the set (loci) of solutions of all polynomials of the type \(x^3+a_2x^2+a_1x+d\), where \( d\in \mathbb R\), can be characterized in terms of hyperbolas. Furthermore, relations between such hyperbolas and Steiner ellipses (inellipses and circumellipses) associated with cubics will be pointed out.

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Authors and Affiliations

  1. Dipartimento di Architettura, Università degli studi di Napoli “Federico II”, Via Toledo, 402-80134, Naples, Italy

    Giuseppina Anatriello

  2. Università di Salerno, via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy

    Giovanni Vincenzi

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  1. Giuseppina Anatriello
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  2. Giovanni Vincenzi
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Correspondence to Giovanni Vincenzi.

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Anatriello, G., Vincenzi, G. Cubics, hyperbolas and steiner ellipses. J. Geom. 112, 45 (2021). https://doi.org/10.1007/s00022-021-00612-4

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  • DOI: https://doi.org/10.1007/s00022-021-00612-4

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