Design, Construction, Painting, and Pricing of a Quadrangular Mosaic with Application of Differential and Integral Calculus Using GeoGebra and Matlab

• DOI: https://doi.org/10.22533/at.ed.3174162407061

• Palavras-chave: Mosaico, geometría euclidiana, cálculo diferencial e integral, segmento, función, área entre curvas, optimización, tarifación.

• Keywords: Mosaic, Euclidean geometry, differential and integral calculus, segment, function, area between curves, optimization, pricing.

• Abstract:

  The objective of the article is that a student, when faced with a mathematical problem related to the design, construction and painting of an abstract art mosaic, can understand the problem posed. Under a constructivist approach, the student must understand the procedure to follow and the tools available to solve it. In this process, the understanding of it is expanded in the algebraic field by applying knowledge of Euclidean geometry and differential and integral calculus. Geometric definitions, such as points, line segments, contours, arc lengths, and areas, are essential. In addition, calculus concepts are explored, such as functions, critical points, local minimums and maximums, optimization and numerical methods to find roots of equations and areas between functions. In a complementary way, the use of scientific software such as GeoGebra allows the student to expand their graphic capacity in the comprehensive design and construction of a work. Regarding the economic valuation of a work of abstract art, the article also addresses how to evaluate a mosaic and apply mathematical concepts related to costing and pricing.