Good knowledge of High School Mathematics.
The discipline encompasses:
- expository classes, appealing to the participation of students;
- classes where the student is expected to present proofs of some theorems and to solve exercises proposed by the teacher.
Get the students familiar with:
- the processes of argumentation/deduction, proof and refutation in Mathematics;
- the arguments, reasoning over pictures, the architecture and writing of convincing arguments based on pictures;
- the visualization of problems and geometric objects; illustrations of the axiomatic viewpoint in plane geometry;
- the theorems and methods of geometry.
The main competencies to develop are: knowledge of mathematical results; generalization and abstraction; to formulate and solve problems; logic argumentation; conception or use of mathematical models to real situations; individual initiative; clear and rigorous written and oral expression; autonomous learning capabilities; imagination and creativity; critical sense; communication skills.
An axiomatic system for Geometry. Congruence and properties of triangles. Circumference properties. The axiom of parallels. Euclidian geometry. Similar triangles. Centers of a triangle. Determination of the measures of a triangle. Area. Isometries. Compass and ruler constructions. Hyperbolic geometry. Parallelism in the hyperbolic plane. Hyperbolic Pythagoras theorem. Area in hyperbolic plane.
António Manuel Freitas Gomes Cunha Salgueiro
Exam or Midterm exam: 100.0%
A. Salgueiro, Geometria, Universidade de Coimbra, 2012
G. E. Martin, The foundation of Geometry and the Non-Euclidian Plane, UTM Springer Verlag, 1998
H. S. M. Coxeter, Introduction to Geometry, 2ª ed, John Wiley & Sons, 1989
P. Araújo, Curso de Geometria, Gradiva, 1998