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In this article, we will give a geometric interpretation of certain finite arithmetic progressions. For this purpose, we will introduce the concept of the n-regular partition { P n } of a quadrilateral. [ABSTRACT FROM AUTHOR]

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/Φ2, Φ2), where Φ2 is the Silver mean. The main result is that in any circle a continue quadrilateral of growth µ can be inscribed for every µ belonging to the interval (1/Φ2, Φ2). Our investigation is supported by dynamical software. [ABSTRACT FROM AUTHOR]