MATEMATICHE COMPLEMENTARI
Academic Year 2018/2019 - 2° Year - Curriculum CCredit Value: 9
Scientific field: MAT/04 - Mathematics education and history of mathematics
Taught classes: 49 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
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).