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Mathematical Communications, Vol. 24 No. 1, 2019.

Original scientific paper

Continue quadrilaterals

Francesco Laudano orcid id orcid.org/0000-0003-4489-095X ; Dipartimento di Matematica, Universit`a di Salerno, Fisciano , Italy
Giovanni Vincenzi orcid id orcid.org/0000-0002-3869-885X ; Dipartimento di Matematica, Universit`a di Salerno, Fisciano, Italy

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Abstract

In this article, we introduce the notion of continue quadrilateral, that is a quadrilateral whose sides are in geometric progression. We obtain an extension of the principal result referring to the growth of continue triangles. Precisely, we will see that the growth of a continue quadrilateral belongs to the interval $(1/\Phi_2, \Phi_2)$, where $\Phi_2$ is the Silver mean. The main result is that in any circle a continue quadrilateral of growth $\mu$ can be inscribed for every $\mu$ belonging to the interval $(1/\Phi_2, \Phi_2)$. Our investigation is supported by dynamical software.

Keywords

Cyclic quadrilaterals; Geometric progressions; Silver mean; Continue quadrilaterals; Growth

Hrčak ID:

215156

URI

https://hrcak.srce.hr/215156

Publication date:

19.4.2019.

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