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A combinatorial interpretation of the Padovan Generalized Polynomial Sequence

The construction of definitions through Padovan's Combinatorial Model: an inves...

A generalização da forma matricial híbrida das sequências de Leonardo, Padovan,...

Relações bi, tri e n-dimensionais de Mersenne

A sequência de Mersenne, batizada em homenagem ao matemático francês Marin Mersenne, é uma progressão recursiva de segunda ordem representada por um modelo unidimensional, cujos números podem ser expressos na forma Mn = 2n-1. Esta pesquisa tem como objetivo explorar e investigar as relações recorrentes em diferentes dimensões, incluindo as bidimensionais (M(n,m)), tridimensionais (M(n,m,p)) e n-dimensionais (M(...

The generalization of Gaussians and Leonardo’s octonions

In order to explore the Leonardo sequence, the process of complexification of this sequence is carried out in this work. With this, the Gaussian and octonion numbers of the Leonardo sequence are presented. Also, the recurrence, generating function, Binet’s formula, and matrix form of Leonardo’s Gaussian and octonion numbers are defined. The development of the Gaussian numbers is performed from the insertion of ...

Leonardo’s bivariate and complex polynomials

Given the purpose of mathematical evolution of Leonardo’s sequence, we have the prospect of introducing complex polynomials, bivariate polynomials and bivariate polynomials around these numbers. Thus, this paper portrays in detail the insertion of the variable x, y and the imaginary unit i in the sequence of Leonardo. Nevertheless, the mathematical results from this process of complexification of these numbers ...

On work and teaching learning: a contribution from the French professional dida...

The French research of the Professional Didactics is substantiated by a confluence zone of three recognized and independent branches of study, namely: Educational Engineering, Cognitive Ergonomics and the Conceptualization of Action Theory. Thus, the present work describes, not exhaustively, certain assumptions, foundations and organizing principles of research in the context of professional training and learni...

The olympic didactical situations (SDOs): teaching mathematical olympiads with ...

The Olympiads of Mathematics acquired an important space in our country, above all, the kind of modality that allows the participation of large numbers of public school students, as in the case of the Brazilian Olympic Games of Mathematics of Public Schools (OBMEP). On the other hand, it is essential to provide, for a larger number of students (non-competitors), an expressive contact with a mathematical culture...

A perspective on the learning and activity of the mathematics teacher: a point ...

The professional activity developed in the teacher's work cannot be considered hermetically as a set of specialized tasks required by a school. On the other hand, when we observe the teacher's activity, from the cognitivist point of view, a large repertoire of knowledge is developed and incorporated in the face of the complex problems inherent in the exercise of the activity. Thus, in the present work, from a p...

Hybridization of triangular numbers: a preliminary and a priori analysis on vis...

This paper discusses the first two phases of Didactic Engineering, supported by the teaching theory, Theory of Didactic Situations, with the aim of developing a study about the hybridization process of triangular numbers, through teaching didactic situations based on the first two Didactic Engineering phases. Considered absent in many contents explored in the area of teaching and in the History of Mathematics, ...