Geometry I

Code: MAT14234L

6 ECTS

Duration: 15 weeks/156 hours

Scientific Area: Mathematics

Teaching languages: Portuguese

Languages of tutoring support: Portuguese

Regime de Frequência: Presencial

Presentation

This is the first curricular unit in Geometry of the degree, where Euclidean geometry is introduced, from an axiomatic point of view as well as other geometries, also from an axiomatic point of view.

Sustainable Development Goals

Educação de qualidade - Assegurar a educação inclusiva, e equitativa e de qualidade, e promover oportunidades de aprendizagem ao longo da vida para todos.

Learning Goals

O1 - Knowledge: experiencing Euclidean geometry, from an axiomatic point of view, workin on som of its fundamental results; contacting other geometries, also through their axioms.
O2 - Skills and Competences: developing abstract reasoning, proof making, and the capacity of finding strategies to solve new problems.

Euclidean geometry on the plane and on the three-dimensional space.
Criteria for congruence of triangles.
Ruler-and-compass constructions.
Ceva's theorem, Menelaus's theorem, Morley's trisector theorem.
Isometries. Similarities.
Symmetry. Symmetry groups.
Axiomatics. Finite geometries.
Circle inversion and the hyperbolic plane.

Teaching Methods

Problem-solving sessions, where students are invited to work on their own or in small groups, with some moments of exposition or discussion involving the whole class.
The evaluation may be either continuous, done through between two and six partial tests and quizzes, done preferably during the classes, weighting 100% of the classification, the number of which is to be defined by the professor who is responsible for the course unit in each academic year, or by a final exam. Students who achieve a grade of 18 or above may have to do an extra oral exam. For these students the final grade is the maximum between 17 and the simple average of the previous grade and the oral exam.
Formative evaluation is done in or by tasks to be done outside class, to improve the learning process; the elements of formative evaluation will have no weight on the final mark.