Geometry

Code:

M1028

Acronym:

M1028

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2019/2020 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:M	131	Official Study Plan	1	-	6	56	162

Teaching language

Suitable for English-speaking students

Objectives

With this course, it is intended that students will know and understand some of the main results of Euclidean geometry that, for its historical importance, should be of general knowledge for mathematicians. In this course the students should also develop their ability to solve geometric problems and to be able to visualize in space.

Learning outcomes and competences

Increased ability to understand and use classical results from geometry. Increased ability to solve problems in a "non-systematic" way. Better visualization of space. Better understanding of space.

Working method

Presencial

Program

Brief reference to a set of axioms (of the type suggested by Birkhoff). Reference to ruler and compass constructions and study of some initial constructions. Notion of congruence and the cases of congruence of triangles. Isometries of the plane. The theorem of Thales. Notion of Area. The Pythagorean theorem. Theorems of Ceva, Menelaus and the angle bisector theorem. Triangle centers. Cases of similarity of triangles and similarity transformations. Construction of the fourth proportional and the mean proportional. Law of sines and law of cosines. Homotheties. Euler's line. Study of the circumference: the inscribed angle theorem; power of a point relative to a circumference. Radical axis of two circles. Possible introduction to the concept of inversion. 

Mandatory literature

Araújo Paulo Ventura; Curso de geometria. ISBN: 972-662-591-2

Complementary Bibliography

Coxeter H. S. M.; Geometry revisited
Moise Edwin E.; Elementary geometry from an advanced standpoint

Comments from the literature

I provide a text

Teaching methods and learning activities

Lectures and classes: The contents of the syllabus are presented in the lectures, where examples are given to illustrate the concepts. There are also practical lessons, where exercises and related problems are solved. 

Software

Geogebra (https://www.geogebra.org/)
Compass and Ruler - Construct and Rule (http://car.rene-grothmann.de/doc_en/)

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	50,00
Teste	50,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

No frequency requirements are required.

Calculation formula of final grade

The content of this course will be divided into two parts, each one evaluated separately. The final grade will be the average of these two parts.

Regular season:
A test will be held during the semester to evaluate the first part of the course content. The regular season exam evaluates only the second part of the course content. I warn that, in the regular season exam, the first part of the course content is not evaluated. Therefore, the test is practically mandatory for those who want to pass the in the regular season.

Second evaluation season:
The second evaluation season exam will be divided into two parts, corresponding to the two parts of the course content, with a short interval of 5 minutes between them. Performing each of these parts is optional except for grade improvement exams (see below). If a student does not perform a part, his grade in that part will be the grade of the regular season. In the performed parts, the student will have the best grade between the grades obtained in the two seasons, unless the grade obtained in the second evaluation season exam is simultaneously lower than the regular season grade and than 5.0 values. In the latter case, the final grade of that part will be the average between the regular season grade and the grade obtained in the second evaluation season: exam.

Special assessment (TE, DA, ...)

Either oral or written examination.

Classification improvement

Students wishing to improve their grade during the regular season will be required to take the test during the semester in addition to the regular season exam. Students wishing to improve their grade at the second evaluation season will need to do both parts of the second evaluation season exam and will not be able to use the grades obtained during the regular season.