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A sequência de Padovan generalizada, números harmoniosos e obras de arte

2023; Sociedade Brasileira de Matemática; Volume: 11; Issue: 32 Linguagem: Inglês

10.21711/2319023x2023/pmo1132

2319-023X

José Antonio Salvador, Ana Manzoli, João Sampaio,

Linguistics and Language Studies

It is possible to expand the school space seeking a more critical performance of students when they visit an exhibition and observe some aspects of a work of art, opening their eyes not only to see its beauty, aesthetics and technique, but also to explore and discover the visible or hidden mathematics that appears in it.The learning of various mathematical contents can be favored when we explore mathematical aspects of works of art, such as geometrical shapes, ratios and proportions, perimeters and areas, linear functions and the like, graphics, polynomial equations and their roots, discrete equations, symmetries, averages, perspectives.In this article we do a analysis of the solutions of the harmonious equations x n -x -1 = 0, of order n ≥ 2, whose positive real roots give us harmonious numbers, especially the golden number (when n = 2) and the plastic number (when n = 3), which have been related to ratios in paintings by impressive painters.