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
The assessment follows either a continuous assessment scheme or a final examination scheme.
Continuous assessment consists of four one-hour tests, to be taken during class. Each test requires a minimum grade of 6 points. The final course grade is the arithmetic average of the grades obtained in the four tests. The student will be considered to have passed if this average is equal to or higher than 9.5 points.
The final examination scheme consists of one written test, in which the student must obtain a minimum of 9.5 points in order to pass the course.
If the student does not pass the course in the regular examination period, or wishes to improve the grade obtained therein, they may sit the resit examination.
At any time deemed necessary, the lecturer may require the student to undertake an oral assessment in order to confirm the grade obtained in the written test.
Continuous assessment consists of four one-hour tests, to be taken during class. Each test requires a minimum grade of 6 points. The final course grade is the arithmetic average of the grades obtained in the four tests. The student will be considered to have passed if this average is equal to or higher than 9.5 points.
The final examination scheme consists of one written test, in which the student must obtain a minimum of 9.5 points in order to pass the course.
If the student does not pass the course in the regular examination period, or wishes to improve the grade obtained therein, they may sit the resit examination.
At any time deemed necessary, the lecturer may require the student to undertake an oral assessment in order to confirm the grade obtained in the written test.
Teaching Staff
- Fátima Maria Filipe Pereira [responsible]
Accreditations and Certifications
