Geometry

Code: MAT11192M

6 ECTS

Duration: 15 weeks/156 hours

Scientific Area: Mathematics

Teaching languages: Portuguese

Languages of tutoring support: Portuguese

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

- Developing a work that encourages a close contact with the axiomatic and proofing in geometry
- Increase the taste for geometry and understanding its close relations to art
- Promote the use of new technologies when dealing with geometric problems.

- Moderns elementary geometry (ulterior developments of Euclidean Geometry)
- Properties of shapes and solids. Geometrical transformations: isometries similarities and inversion.
- Symmetry of an object and its relation with art and architecture.
- Cyclic and dihedral groups, friezes and patterns.
- Study of symmetries of solids through models obtained from their planifications.
- Projective geometry and evolution of perspective in painting.
- Hyperbolic geometry and study of the Poincaré model using inversion

Teaching Methods

Expository classes of the subjects with examples. Practical laboratorial classes for resolution of exercises using computer software.
Practical simulation of classes.
One final exam. A report discution