# CLASSICAL GEOMETRY

## Learning outcomes of the course unit

The aim of this course is to provide students with essentials tools in Euclidean Geometry in the plane and in the space; students are requested also to apply their knowledge and understanding to problems concerning the spatial structure of real environment, graphical and architectonic structures.

The aim of this course is to provide students with essentials tools in Euclidean Geometry in the plane and in the space; students are requested also to apply their knowledge and understanding to problems concerning the spatial structure of real environment, graphical and architectonic structures.

## Prerequisites

Geometry 1 and Algebra

Geometry 1 and Algebra

## Course contents summary

ISOMETRIES IN THE EUCLINEAN PLANE AND SPACE.

POLYGONS AND THEIR SYMMETRY GROUPS. CIRCLES AND TRIANGLES.

TILINGS THE PLANE AND SYMMETRY GROUPS. TILINGS AND PATTERNS GROUPS.

POLYEDRA, REGULAR POLYHEDRA AND THEIR SYMMETRY GROUPS. FINITE GROUPS OF SPACE ISOMETRIES.

ISOMETRIES IN THE EUCLINEAN PLANE AND SPACE.

POLYGONS AND THEIR SYMMETRY GROUPS. CIRCLES AND TRIANGLES.

TILINGS THE PLANE AND SYMMETRY GROUPS. TILINGS AND PATTERNS GROUPS.

POLYEDRA, REGULAR POLYHEDRA AND THEIR SYMMETRY GROUPS. FINITE GROUPS OF SPACE ISOMETRIES.

## Course contents

ISOMETRIES IN THE EUCLINEAN PLANE AND SPACE.

POLYGONS AND THEIR SYMMETRY GROUPS. CIRCLES AND TRIANGLES.

TILINGS THE PLANE AND SYMMETRY GROUPS. TILINGS AND PATTERNS GROUPS.

POLYEDRA, REGULAR POLYHEDRA AND THEIR SYMMETRY GROUPS. FINITE GROUPS OF SPACE ISOMETRIES.

## Recommended readings

M. DEDO', FORME, ED. ZANICHELLI 1999.

Notes by the teacher.

M. DEDO', FORME, ED. ZANICHELLI 1999.

Notes by the teacher.

## Teaching methods

In the lectures we shall propose formal definitions and proofs, with significant examples and applications, and several exercises. Exercises are an essential tool in Euclidean Geometry; they are often proposed to be done by the students themselves, to learn how to apply their knowledge to particular cases.

In the lectures we shall propose formal definitions and proofs, with significant examples and applications, and several exercises. Exercises are an essential tool in Euclidean Geometry; they are often proposed to be done by the students themselves, to learn how to apply their knowledge to particular cases.

## Assessment methods and criteria

Learning is checked in a classic way, through the evaluation of a written exam and an oral interview.

In the written exam, through the exercises, students must exhibite basic knowledge related to Euclidean Geometry. In addition, students will be required to apply their knowledge to particular cases.

In the colloquium, students must be able to prove properties of the studied structures, using an appropriate geometric and algebraic language and a proper mathematical formalism.

Learning is checked in a classic way, through the evaluation of a written exam and an oral interview.

In the written exam, through the exercises, students must exhibite basic knowledge related to Euclidean Geometry. In addition, students will be required to apply their knowledge to particular cases.

In the colloquium, students must be able to prove properties of the studied structures, using an appropriate geometric and algebraic language and a proper mathematical formalism.