Continue quadrilaterals
Laudano, Francesco ; Vincenzi, Giovanni
Mathematical Communications, Tome 23 (2018) no. 2, p. 133-146 / Harvested from Mathematical Communications
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.
Publié le : 2018-12-05
Classification:  Cyclic quadrilaterals; Geometric progressions; Silver mean; Continue quadrilaterals; Growth.,  51 M 05; 51 M 15; 51 N 20.
@article{mc2756,
     author = {Laudano, Francesco and Vincenzi, Giovanni},
     title = {Continue quadrilaterals},
     journal = {Mathematical Communications},
     volume = {23},
     number = {2},
     year = {2018},
     pages = { 133-146},
     language = {eng},
     url = {http://dml.mathdoc.fr/item/mc2756}
}
Laudano, Francesco; Vincenzi, Giovanni. Continue quadrilaterals. Mathematical Communications, Tome 23 (2018) no. 2, pp.  133-146. http://gdmltest.u-ga.fr/item/mc2756/