The most influential books on geometry are those of Euclid called "Elements". In our century, in addition to classical learning, various interactive software are used in teaching geometry. Among them, we can mention Geogebra. GeoGebra is an interactive math measurement program that consists of teaching and learning from elementary to university level. This software is offered as a pedagogical and mathematical aid tool. GeoGebra helps in teaching math because using this software, students see different mathematical formulas, algebraic and geometric presentations. In this paper, using GeoGebra software, the pedagogical, methodological, and statistical data into teaching circle properties are presented. The study involved 112 students. Of these 40% excellent, 35% average, 25% below average. The research aims to prepare high school students aged 15-18, from grades 1, 2, 3, and 4 in teaching, working, and explaining geometry through Geogebra software. Special emphasis is placed on the circle properties and their presentations. This content includes the district tangent, the potency, the application of the circle in regular polygons with special emphasis on the inscribed, circumscribed circle in the equilateral triangle, and other important properties.
In this paper we introduce a bivariate of q-Durrmeyer variant of generalized Bernstein operators by using Pólya distribution. The convergence rate of these operators is examined by means of the Lipschitz class and the modulus of continuity. Furthermore, we obtain a Voronovskaja type symptotic formula, error estimation in terms of the partial modulus of continuity and Peetre's K-functional.
An equivalent form of Nikol'skii class (H(p, k, ϕ), p ∈ [1, ∞]) using a supplementary condition for function ϕ and best approximation is given. The estimation of Fourier coefficients of functions belonging to the class H(p, k, ϕ), p ∈ [1, ∞], by means of best approximation and modulus of smoothness without giving supplementary conditions to the ϕ function is investigated. We discuss the problem for the functions with quasi-monotone Fourier coefficients as well.2010 Mathematics Subject Classification. Primary: 42A16.
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