Geometry

Recommended Prerequisites

Good knowledge of High School Mathematics.

Teaching Methods

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.

Learning Outcomes

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.

Work Placement(s)

No

Syllabus

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.

Head Lecturer(s)

António Manuel Freitas Gomes Cunha Salgueiro

Assessment Methods

Assessment
Exam or Midterm exam: 100.0%

Bibliography

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