Solução dos três problemas clássicos da matemática grega por curvas mecânicas

Abstract

This study aims at displaying the beginning of the development of Mathematics, within a geometrical perspective, covering the methods of resolution, known today as the three classical problems of the Greek Mathematics: squaring the circle, trisecting the angle and doubling the cube. Besides that, this dissertation talks about the work of some great mathematicians of the ancient times, who are Archimedes, Dinostrato, Eratosthenes, Hippias, Pappus and Nicomedes. These mathematicians leaned over the referred problems and o ered very elegant solutions, by means of the use of mechanical curves, such as the quadratrix or trisectrix, the conchoids and the cissoids, although the desired ones, initially, were the so called Euclidean constructions, that is, the constructions done only with ruler and a compass. In this work, it is also presented the neusis constructions, responsible for a signi cant part of the trisection solutions. This work can help others who are interested in the matter, once it shows the importance of geometry for the fostering of the development of all Mathematical knowledge.