Construções euclidianas e o desfecho de problemas famosos da geometria

• Autor(a) principal: Precioso, Juliana Conceição [UNESP]
• Data de Publicação: 2011
• Outros Autores: Pedroso, Hermes Antonio [UNESP]
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://revistas.unicentro.br/index.php/RECEN/article/view/1384; http://hdl.handle.net/11449/122395
• topic: números construtíveis; números algébricos; Números Transcendentes; Polígonos regulares; algebraic and transcendental numbers; constructible numbers; regular polygons

Construction techniques with ruler and the compasses, fundamental on Euclidean geometry, have been related to modern algebraic theories such as solving equations and extension of bodies from the works by Paolo Ruffini (1765-1822), Niels Henrik Abel (1802-1829) and Evariste Galois (1811-1832). This relation could provide an answer to some famous problems, from ancient Greece, such as doubling the cube, the trisection Angle, the Quadrature of the Circle and the construction of regular polygons, which remained unsolved for over two thousand years. Also important for our purposes are the notions of algebraic numbers, transcendental and the criteria for constructability, of those numbers. The objective of this study is to reconstruct relevant steps of geometric constructions with ruler (unmarked) and the compasses, from the elementary to the outcome buildings, in the nineteenth century, considering those mentioned problems.