Geometry

Cod: 21165

Department: DCET

Department: DCET

ECTS: 6

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 156

Total contact time: 26

Total contact time: 26

In this unit we introduce Birkhoff’s axiomatics for Euclidian geometry.

Euclidian geometry

Birkhoff’s axiomatics

Birkhoff’s axiomatics

By the end of the course the student should be able to prove the basic results of Euclidian geometry, providing the appropriate justification of each inference in terms of the axioms previously introduced.

1. History of geometry.

2. Some preliminaries of logic.

3. Incidence spaces.

4. Distance axioms.

5. Separation axiom.

6. Congruences of triangles, existence of paralels and the Saccheri-Legendre Theorem.

7. The Pythagorean theorem and its converse.

8. Circumferences, ruler and compass constructions.

9. Isometries

2. Some preliminaries of logic.

3. Incidence spaces.

4. Distance axioms.

5. Separation axiom.

6. Congruences of triangles, existence of paralels and the Saccheri-Legendre Theorem.

7. The Pythagorean theorem and its converse.

8. Circumferences, ruler and compass constructions.

9. Isometries

A. J. Franco Oliveira, Geometrias, Universidade de Évora, 2004.

A. J. Franco Oliveira, Geometria Euclidiana, Universidade Aberta, 1995.

A. J. Franco Oliveira, Transformações Geométricas, Universidade Aberta, 1997.

Paulo Ventura Araújo, Curso de Geometria, Gradiva, 1999.

A. J. Franco Oliveira, Geometria Euclidiana, Universidade Aberta, 1995.

A. J. Franco Oliveira, Transformações Geométricas, Universidade Aberta, 1997.

Paulo Ventura Araújo, Curso de Geometria, Gradiva, 1999.

E-Learning.

Continuous assessment is privileged: 2 or 3 digital written documents (e-folios) during the semester (40%) and a
presence-based final exam (p-folio) in the end of the semester (60%). In due time, students can alternatively choose to perform one
final presence-based exam (100%).