Banca de DEFESA: WALDECK SILVA SOUZA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : WALDECK SILVA SOUZA
DATE: 27/06/2023
TIME: 14:00
LOCAL: Auditório 801 no 8º andar do Bloco B do Campus Santo André da Universidade Federal do ABC
TITLE:

Plane Geometry: Axiomatic Foundations

PAGES: 120
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUBÁREA: Geometria e Topologia
SUMMARY:

Our main objectives in the present work are to present the axiomatic systems of Birkhoff and Hilbert, to present some important results of neutral geometry, the discussions about the fifth postulate of Euclid as well as the several attempts of its demonstration from the first four postulates, the hyperbolic geometry and contribute in some way to the teaching of Euclidean, neutral and hyperbolic geometry (the latter two, by way of enrichment or suggestion) in high school.

We take an important step towards a possible demonstration of the equivalence of Hilbert's and Birkhoff's system of axioms, as we demonstrate that Birkhoff's axioms imply Hilbert's axioms and present an almost complete proof that Hilbert's axioms imply Birkhoff's axioms.

COMMITTEE MEMBERS:
Presidente - Interno ao Programa - 1734928 - SINUE DAYAN BARBERO LODOVICI
Membro Titular - Examinador(a) Interno ao Programa - 2604830 - MARCIO FABIANO DA SILVA
Membro Titular - Examinador(a) Externo à Instituição - ALEXANDRE LYMBEROPOULOS - USP
Membro Suplente - Examinador(a) Interno ao Programa - 1475468 - RAFAEL DE MATTOS GRISI
Membro Suplente - Examinador(a) Externo à Instituição - GLEICIANE DA SILVA ARAGÃO - UNIFESP