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Abstract(s)
As equações e os seus métodos de resolução são essenciais em todas as áreas e todos os níveis de escolaridade. Historicamente, resolver equações sempre foi de grande importância para os matemáticos e, essas equações, apareciam quase sempre como consequência da resolução de problemas. Este trabalho consiste em estudar, analisar e explicitar, na medida do possível, os momentos mais relevantes na história das equações algébricas. Esta abordagem incidirá numa área temporal de vários séculos, do Egito ao Renascimento Europeu. Pouco a pouco foi-se definindo o conceito de equação e a Álgebra começa a ser entendida como o estudo da resolução de equações. Em 1842, Nesselmann considerou que podem ser reconhecidos três estágios no desenvolvimento histórico da Álgebra. Primeiro, temos o primitivo ou retórico, em que os argumentos da resolução de um problema são escritos em prosa pura, sem abreviações ou símbolos específicos, como foi o caso dos egípcios e dos babilónios. A seguir, vem um estágio intermediário, sincopado, na qual se adotam abreviações para algumas das quantidades e operações que se repetem mais frequentemente. A Aritmética de Diofanto deve ser colocada nesta categoria. A partir do século XVI entrou-se numa nova etapa, a da álgebra simbólica. Nesta época, dão-se grandes progressos na resolução de equações, as quais se expressam numa espécie de taquigrafia matemática formada de símbolos que, aparentemente, nada tem a ver com os entes que representam. Scipione del Ferro é o primeiro a resolver a equação geral do 3.º grau. No entanto, não publica os seus resultados, e a mesma descoberta é feita por Tartaglia e publicada por Cardano, na sua Ars Magna. Por fim, a equação geral do 4.º grau é resolvida por Ferrari.
Equations and their methods of resolution are essential in all areas and at all levels of schooling. Historically solving equations has always been of great importance to mathematicians, and these equations almost always appeared as a consequence of problem solving. This work consists of studying, analyzing and explaining, as far as possible, the most relevant moments in the history of algebraic equations. This approach will focus on a time span of several centuries, from Egypt to the European Renaissance. Little by little the concept of equation was defined and Algebra begins to be understood as the study of the resolution of equations. In 1842, Nesselmann considered that three stages can be recognized in the historical development of Algebra. First, we have the primitive or rhetorical, in which the arguments for solving a problem are written in pure prose, without abbreviations or specific symbols, as was the case of the Egyptians and the Babylonians. Next comes an intermediate stage, syncopated, in which abbreviations are adopted for some of the quantities and operations that are repeated more frequently. Diophantine Arithmetic should be placed in this category. From the sixteenth century entered a new stage, that of symbolic algebra. At this time, great progress has been made in solving equations, which are expressed in a kind of mathematical shorthand composed of symbols that apparently have nothing to do with the entities they represent. Scipione del Ferro is the first to solve the general equation of the third degree. However, it does not publish its results, and the same finding is made by Tartaglia and published by Cardano in his Ars Magna. Finally, the general equation of the fourth degree is solved by Ferrari.
Equations and their methods of resolution are essential in all areas and at all levels of schooling. Historically solving equations has always been of great importance to mathematicians, and these equations almost always appeared as a consequence of problem solving. This work consists of studying, analyzing and explaining, as far as possible, the most relevant moments in the history of algebraic equations. This approach will focus on a time span of several centuries, from Egypt to the European Renaissance. Little by little the concept of equation was defined and Algebra begins to be understood as the study of the resolution of equations. In 1842, Nesselmann considered that three stages can be recognized in the historical development of Algebra. First, we have the primitive or rhetorical, in which the arguments for solving a problem are written in pure prose, without abbreviations or specific symbols, as was the case of the Egyptians and the Babylonians. Next comes an intermediate stage, syncopated, in which abbreviations are adopted for some of the quantities and operations that are repeated more frequently. Diophantine Arithmetic should be placed in this category. From the sixteenth century entered a new stage, that of symbolic algebra. At this time, great progress has been made in solving equations, which are expressed in a kind of mathematical shorthand composed of symbols that apparently have nothing to do with the entities they represent. Scipione del Ferro is the first to solve the general equation of the third degree. However, it does not publish its results, and the same finding is made by Tartaglia and published by Cardano in his Ars Magna. Finally, the general equation of the fourth degree is solved by Ferrari.
Description
Tese de mestrado, Matemática para Professores, Universidade de Lisboa, Faculdade de Ciências, 2017
Keywords
História da matemática Equações algébricas Álgebra Resolução de problemas Problemas históricos Teses de mestrado - 2017