The Bivariate (Complex) Fibonacci and Lucas Polynomials: An Historical Investigation with the Maple's Help

Autor/inn/en	Alves, Francisco Regis Vieira; Catarino, Paula Maria Machado Cruz
Titel	The Bivariate (Complex) Fibonacci and Lucas Polynomials: An Historical Investigation with the Maple's Help
Quelle	In: Acta Didactica Napocensia, 9 (2016) 4, S.71-95 (25 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2065-1430
Schlagwörter	Mathematical Models; Numbers; Algebra; Mathematical Formulas; Logical Thinking; Comparative Analysis; Computer Software + Suchen Sie Ihr Suchwort? Mathematical model; Mathematisches Modell; Zahlenraum; Mathematische Formel
Abstract	The current research around the Fibonacci's and Lucas' sequence evidences the scientific vigor of both mathematical models that continue to inspire and provide numerous specializations and generalizations, especially from the sixties. One of the current of research and investigations around the Generalized Sequence of Lucas, involves it's polinomial representations. Therefore, with the introduction of one or two variables, we begin to discuss the family of the Bivariate Lucas Polynomias (BLP) and the Bivariate Fibonacci Polynomials (BFP). On the other hand, since it's representation requires enormous employment of a large algebraic notational system, we explore some particular properties in order to convince the reader about an inductive reasoning that produces a meaning and produces an environment of scientific and historical investigation supported by the technology. Finally, throughout the work we bring several figures that represent some examples of commands and algebraic operations with the CAS Maple that allow to compare properties of the Lucas' polynomials, taking as a reference the classic of Fibonacci's model that still serves as inspiration for several current studies in Mathematics. (As Provided).
Anmerkungen	Babes-Bolyai University. Kogainiceanu 1, Cluj-Napoca, 400084 Romania. e-mail: submit_adn@yahoo.com; Web site: http://adn.teaching.ro
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01