In this article, we will show that for every choice of real numbers a1 and a2, the set (loci) of solutions of all polynomials of the type x3+ a2x2+ a1x+ d, where d∈ 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.
Cubics, hyperbolas and steiner ellipses / Anatriello, G.; Vincenzi, G.. - In: JOURNAL OF GEOMETRY. - ISSN 0047-2468. - 112:3(2021). [10.1007/s00022-021-00612-4]
Cubics, hyperbolas and steiner ellipses
Anatriello G.;Vincenzi G.
2021
Abstract
In this article, we will show that for every choice of real numbers a1 and a2, the set (loci) of solutions of all polynomials of the type x3+ a2x2+ a1x+ d, where d∈ 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.File in questo prodotto:
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