2023
Geometry
Name: Geometry
Code: MAT11192M
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Regime de Frequência: Presencial
Sustainable Development Goals
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.
- Increase the taste for geometry and understanding its close relations to art
- Promote the use of new technologies when dealing with geometric problems.
Contents
- 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
- 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
Practical simulation of classes.
One final exam. A report discution
Teaching Staff
- Rui Pedro Lima Pinto Ribeiro de Albuquerque [responsible]
