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Advisor(s)
Abstract(s)
Os chineses inventaram o papel e, na idade média, no Japão, começou a ser desenvolvido um
conjunto de técnicas de dobragens de papel, designado por Origami. Já no século XX, estas
técnicas despertaram o interesse de diversos matemáticos. H. Huzita, K. Hatori e R. Lang fixaram
o sistema axiomático para as construções com dobragens. Na presente dissertação, apresenta-se
este sistema axiomático e a resolução dos problemas clássicos da duplicação do cubo e da trisecção
de um ângulo com Origami. Além disso, estuda-se a teoria dos números construtíveis com Origami
em comparação com a teoria dos números construtíveis com régua e compasso.
The Chinese invented the paper and, in the middle ages, in Japan, a set of folding techniques began to emerge: the Origami. Recently, in 20th century, these techniques attracted the attention of several mathematicians. H. Huzita, K. Hatori and R. Lang established an axiomatic system for Origami constructions. In the present dissertation, we present this axiomatic system and the resolution of the classic problems of doubling the cube and angle trissection with Origami. Besides that, we study the theory of Origami's constructible numbers in comparison with the theory of constructible numbers with non-graduated ruler and compass.
The Chinese invented the paper and, in the middle ages, in Japan, a set of folding techniques began to emerge: the Origami. Recently, in 20th century, these techniques attracted the attention of several mathematicians. H. Huzita, K. Hatori and R. Lang established an axiomatic system for Origami constructions. In the present dissertation, we present this axiomatic system and the resolution of the classic problems of doubling the cube and angle trissection with Origami. Besides that, we study the theory of Origami's constructible numbers in comparison with the theory of constructible numbers with non-graduated ruler and compass.
Description
Keywords
Axiomas de Huzita-Hatori Duplicação do Cubo Números Construtíveis Origami Régua e Compasso Trissecção do Ângulo