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Master's Dissertation
DOI
10.11606/D.55.2019.tde-22032019-162007
Document
Author
Full name
Caio Eduardo Martins Raiz
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2018
Supervisor
Committee
Picon, Tiago Henrique (President)
Lopes, Pedro Tavares Paes
Pereira, Jamil Viana
Zani, Sergio Luis
Title in Portuguese
Transformações de Mobius e projeções na esfera de Riemann
Keywords in Portuguese
Geometria analítica em C
Números complexos
Projeções na esfera de Riemann
Transformações de mobius
Abstract in Portuguese
Nessa dissertação exploramos os efeitos geométricos das Transformações de Möbius em C utilizando projeções na Esfera de Riemann. Como aplicação, apresentamos a ação de algumas transformações aplicadas em cônicas no plano. Uma atividade didática voltada aos alunos do Ensino Médio sobre Transformações de Möbius utilizando o Geogebra é apresentada.
Title in English
Mobius Transformations and Riemann Sphere Projections
Keywords in English
Analytic geometric in C
Complex numbers
Mobius transformations
Riemann sphere projections
Abstract in English
In the course of this dissertation we explore the geometric effects of the Möbius Transforms in C using projections in the Riemann sphere. As an application, we present the action of some transformations applied on conics in the plane. A didactic activity aimed at high school students about Möbius Transformations using Geogebra is presented.
 
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Publishing Date
2019-03-22
 
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