Geometries and isometries: of Hilbert's postulates to the hyperbolic plane

• Grant number: 13/03036-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2013
• End date: June 30, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Henrique Nogueira de Sá Earp
• Grantee: Diana Terezinha Amaro
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The student will study, from Hilbert's axiomatic, the segments arithmetic, with emphasis to critical analysis of the postulates of the Ruler and Protractor, found in the literature. Then will address the concept of a group of isometries, passing of the Euclidean case already known for the non-Euclidean geometries, with emphasis on the Möbius group. If have time, the student will discuss the topological classification of surfaces. (AU)