2025
Elements of geometry
Name: Elements of geometry
Code: MAT14990L
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
1 Identify flat geometric figures, as well as explore the various geometric properties in the plane that allow activities to be developed in the classroom context.
2 Identify several geometric solids, as well as their properties, some associated topological notions, and important relationships verified by them.
3 Understand the notion of geometric transformation, as well as its properties. Recognize and apply the various isometries, as well as the various similarities and applications thereof.
4 Ability to calculate lengths, areas and volumes, in different contexts, as well as recognizing the importance of their applications in the classroom.
5.Acquire skills to formulate and solve problems within the scope and/or with geometry techniques.
6. Relate concepts from other areas of mathematics and other disciplines with geometry concepts.
2 Identify several geometric solids, as well as their properties, some associated topological notions, and important relationships verified by them.
3 Understand the notion of geometric transformation, as well as its properties. Recognize and apply the various isometries, as well as the various similarities and applications thereof.
4 Ability to calculate lengths, areas and volumes, in different contexts, as well as recognizing the importance of their applications in the classroom.
5.Acquire skills to formulate and solve problems within the scope and/or with geometry techniques.
6. Relate concepts from other areas of mathematics and other disciplines with geometry concepts.
Contents
A1 Geometry in the plane. Figures and elements: points, lines, segments. Polygons, circles. Parabolas, ellipses.
A2 Geometry in space. Polyhedra. Surfaces.
B1 Notions of topology. Revisited graphs and polyhedra. Euler characteristic.
B2 Knots and braids. Enumeration. Moebius bands, Klein bottle.
B3 Examples using folding.
C1 Geometric Transformations in the Plane. Isometries: translation, rotation, reflection, sliding reflection. Group of displacements, group of isometries.
C2 Symmetries, friezes, generators of symmetric groups.
C3 Similarities: homotheties, transformations of similarities, some special forms.
D1 Measurements. Areas and Volumes. Calculations of areas and volumes of geometric figures.
D2 System of units. Measurement of quantities: lengths, areas and volumes.
A2 Geometry in space. Polyhedra. Surfaces.
B1 Notions of topology. Revisited graphs and polyhedra. Euler characteristic.
B2 Knots and braids. Enumeration. Moebius bands, Klein bottle.
B3 Examples using folding.
C1 Geometric Transformations in the Plane. Isometries: translation, rotation, reflection, sliding reflection. Group of displacements, group of isometries.
C2 Symmetries, friezes, generators of symmetric groups.
C3 Similarities: homotheties, transformations of similarities, some special forms.
D1 Measurements. Areas and Volumes. Calculations of areas and volumes of geometric figures.
D2 System of units. Measurement of quantities: lengths, areas and volumes.
Teaching Methods
Classes in theoretical-practical format, expository of content, articulated with the presentation of examples and exercises. The presentation moments alternate with the presentation of applications and discussion on solving associated problems. Applications can be proposed and presented by students and can be related to geometry or other disciplinary areas. Moments to perform exercises in groups and individually. Calls to the board for students to present concepts and solve problems to their colleagues. It is suggested to use free-to-use geogebra software or another software to be decided by the teacher when solving certain problems. In this way, the recommendations and guidelines of the pedagogical model of the university of Évora are taken into account.
Assessment
Continuous assessment regime or a final exam assessment regime.
Continuous assessment will consist of several short moments - questions in class, with these assessment moments seen as a mix of assessment and practice/learning moments. They can be held every week or with a schedule to be agreed by the teacher at the beginning of the academic year. These moments must be more than 5 throughout the semester (1/3 of the total number of weeks).
In addition to the questions in class, a final written test will be carried out.
Each question in will have a fixed price (e.g. 2 points). The final grade for questions in is obtained by adding the partial grades for each question and normalized to 20 points. The weight of questions in will be 30% of the final grade. The final test will weigh 70% of the final grade.
Continuous assessment will consist of several short moments - questions in class, with these assessment moments seen as a mix of assessment and practice/learning moments. They can be held every week or with a schedule to be agreed by the teacher at the beginning of the academic year. These moments must be more than 5 throughout the semester (1/3 of the total number of weeks).
In addition to the questions in class, a final written test will be carried out.
Each question in will have a fixed price (e.g. 2 points). The final grade for questions in is obtained by adding the partial grades for each question and normalized to 20 points. The weight of questions in will be 30% of the final grade. The final test will weigh 70% of the final grade.
Teaching Staff
- Fátima Maria Filipe Pereira [responsible]
Certificações
