# MATEMATICHE COMPLEMENTARI

**Academic Year 2021/2022**- 2° Year - Curriculum DIDATTICO

**Teaching Staff:**

**Mario PENNISI**

**Credit Value:**6

**Scientific field:**MAT/04 - Mathematics education and history of mathematics

**Taught classes:**28 hours

**Exercise:**24 hours

**Term / Semester:**2°

## Learning Objectives

Understanding of a statement, ability to construct rigorous demonstrations of theorems, ability to express oneself with language properties, to be able to apply the acquired knowledge to proposed problems.

## Course Structure

The lessons will be participated and / or cooperative. Practical exercises, laboratory tests, group work, educational experiences in the field are planned.

If the teaching is given in a mixed or remote way, the necessary changes may be introduced with respect to what was previously stated, in order to respect the program envisaged and reported in the syllabus.

## Detailed Course Content

The Erlangen Program. Geometry of the plane according to Klein. The concept of equality. Affinity of the Euclidean plane. Affinity properties. Equality by affinity. Examples of affinity. Classification of affinities. The group of similarities. Properties of similarities. Equality by similarities. Dilatations. The group of isometries. Offsets. Rotations. Orthogonal symmetries. Other types of similarities. Search for joined points in a simile. Classification of similarities. Similar products. Sets of generators. Notable subgroups of the group of similarities. Applications of geometric transformations to elementary geometry. Use of DGS.

## Textbook Information

- Cassina U.;
*Trasformazioni geometriche elementari*, in Enciclopedia delle matematiche elementari e complimenti a cura di Berzolari L., Vivanti G., Gigli D., vol. 2° parte prima Hoepli Milano 1937 - Dedò M.;
*Trasformazioni geometriche*. Decibel Zanichelli 1996 - Modenov, P. S.; Parkhomenko, A. S. (1965) .
*Geometric Transformations*(2 vols.):*Euclidean and Affine Transformations*, and*Projective Transformations*. New York: Academic Press. - Yaglom, I. M. (1962, 1968, 1973, 2009) .
*Geometric Transformations*(4 vols.). Random House (I, II & III), MAA (I, II, III & IV).