Aplicações para o princípio de indução matemática
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2014-09-26
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Universidade Federal de Goiás
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This paper sought to systematically present knowledge on the number theory in a clear and acessible way to a broader community than the mathematical academics, the principle of mathematical induction PMI, was the background and the main tool to all demonstrations so to permeate almost all the results and, in each section, at least one numerical example was given, thus making it easier to readers beginning their studies in math and always seeking to at least encourage the investigative feeling on all readers. The continuous fractions, subject commonly overlooked, yet with vast applications in Physics and Calculus, proved to be familiar with the Fibonacci numbers. Sequentially, two classic game problems were presented, The Hanoi Tower and the problem of the false coin, which could, from simple examples be generalized demonstrating solutions for the problems at any given natural number. Finally, the linear recurrences of second order and the higher order arithmetic progression were shown to have deep connections with the Fibonacci sequence, so then, these numbers became the main motivators for all the paper, that prizes for demonstrable results through PMI or related to this sequence of numbers, and always sought to strengthen the admiration of the dialogues with branches apparently so fixed that are the familiar through the appearance of the Fibonacci numbers in these topics.
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SILVA JUNIOR, N. Aplicações para o princípio de indução matemática. 2014. 54 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2014.