# Geometry

Year
1
2018-2019
Code
01001121
Subject Area
Mathematics
Language of Instruction
Portuguese
Mode of Delivery
Face-to-face
Duration
SEMESTRIAL
ECTS Credits
6.0
Type
Compulsory
Level
1st Cycle Studies

## Recommended Prerequisites

Good knowledge of High School Mathematics.

## Teaching Methods

The discipline encompasses:

- expository classes, appealing to the participation of students;

- classes where the student is expected to present proofs of some theorems and to solve exercises proposed by the teacher.

## Learning Outcomes

Get the students familiar with:

- the processes of argumentation/deduction, proof and refutation in Mathematics;

- the arguments, reasoning over pictures, the architecture and writing of convincing arguments based on pictures;

- the visualization of problems and geometric objects; illustrations of the axiomatic viewpoint in plane geometry;

- the theorems and methods of geometry.

The main competencies to develop are: knowledge of mathematical results; generalization and abstraction; to formulate and solve problems; logic argumentation; conception or use of mathematical models to real situations; individual initiative; clear and rigorous written and oral expression; autonomous learning capabilities; imagination and creativity; critical sense; communication skills.

No

## Syllabus

An axiomatic system for Geometry. Congruence and properties of triangles. Circumference properties. The axiom of parallels. Euclidian geometry. Similar triangles. Centers of a triangle. Determination of the measures of a triangle. Area. Isometries. Compass and ruler constructions. Hyperbolic geometry. Parallelism in the hyperbolic plane. Hyperbolic Pythagoras theorem. Area in hyperbolic plane.

António Manuel Freitas Gomes Cunha Salgueiro

## Assessment Methods

Assessment
Exam or Midterm exam: 100.0%

## Bibliography

A. Salgueiro, Geometria, Universidade de Coimbra, 2012

G. E. Martin, The foundation of Geometry and the Non-Euclidian Plane, UTM Springer Verlag, 1998

H. S. M. Coxeter, Introduction to Geometry, 2ª ed, John Wiley & Sons, 1989

P. Araújo,  Curso de Geometria, Gradiva, 1998