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Resumo: O presente artigo apresenta uma abordagem de investigacao no contexto da Historia da Matematica, envolvendo situacoes que visam oportunizar o entendimento da extensao, evolucao e generalizacao de propriedades da Sequencia de Fibonacci. Dessa forma, abordam-se duas situacoes. A primeira, envolvendo a descricao da formula de Binnet no campo dos inteiros. Logo em seguida, apresenta-se uma descricao e analise dos termos explicitos presentes na Sequencia Polinomial de Fibonacci. O escopo da presente proposta de atividade busca a divulgacao cientifica de nocoes envolvendo a generalizacao, ainda atual, fato que acentua o carater ubiquo da Sequencia de Fibonacci. A vista disso, a proposta de experimento didatico esta fundamentada na organizacao das caracteristicas da Engenharia Didatica. Almeja-se, alem da validacao interna das hipoteses levantadas durante a investigacao, contribuir com a formacao inicial de estudantes dos cursos de Licenciatura em Matematica que virem a estudar o tema. Palavras-chave: Atividades de investigacao. Engenharia Didatica. Historia da Matematica. Sequencia Generalizada de Fibonacci. THE STUDY OF MATHEMATICAL DEFINITIONS IN THE CONTEXT OF HISTORICAL RESEARCH: A DIDACTIC EXPERIMENT INVOLVING DIDACTIC ENGINEERING AND FIBONACCI POLYNOMIAL SEQUENCES Abstract: This article presents a research approach within the context of History of Mathematics, involving situations that aim to provide an understanding of the extension, evolution and generalization of properties of the Fibonacci Sequence. In this way, two situations are addressed. The first, involving the description of Binet's formula in the integer field. Then, a description and analysis of the explicit terms present in the Fibonacci Polynomial Sequence is presented. The scope of this activity proposal seeks the scientific dissemination of notions involving generalization, still current, a fact that accentuates the ubiquitous character of the Fibonacci Sequence. Thus the proposal of didactic experiment is based on the organized in the characteristics of Didactic Engineering, beyond the internal validation of the hypotheses raised during the investigation this paper aims at contributing to initial education of undergrad   Mathematicsof students that may come to study the subject. Keywords: Research activities. Didactic Engineering. History of Mathematics. Generalized Fibonacci Sequence.

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O estudo de definições matemáticas no contexto de investigação histórica: um experimento didático envolvendo Engenharia Didática e Sequências Polinomiais de Fibonacci