Revisão histórica de soluções geométricas do problema da quadratura do círculo

Abstract

At this study, we review some of the main geometric solutions in squaring the circle, having a free translation into Portuguese of some articles related to the squaring of the circle second Hobson[5] e analyzing their in uence throughout history in the evolution of mathematics. In this work we try to understand how the problem of squaring the circle is presented throughout history, began reviewing the main registers of the problem, from the century V a-C. Then we wrote a theoretical foundation of squaring the circle and the determination of , displaying ancient accounts of quadrature in dependence on the transcendence of this irrational number. Next, we write some contributions of ancient civilizations, which is cited the work of the Greeks, before and after Archimedes, as well as approximations determined by Indian, Chinese and Arabic. In the Renaissance period we nd mathematicians such as Leonardo Pisano, George Purbach and Cardinal Nicholas of Cusa, which they used the Archimedes method and obtained better results for approach . In the fteenth and sixteenth centuries, with advances in trigonometry introduced by Copernicus, Rheticus, Pitiscus and Johannes Kepler allowed the problem of squaring the circle had a better approach. In this period we reviewed the studies of Snellius and Huygens, the theorems of Huygens and Gregory's work. In the nal part of this work we selected some constructions of recti cation and squaring the circle. Among them stand out: the squaring the circle by Descartes and another by Ramanujan, both with intereszing results.