# Elements od complementary mathematics

**Academic Year 2018/2019**- 1° Year - Curriculum DIDATTICO

**Teaching Staff**

- MATEMATICHE ELEMENTARI DA UN PUNTO DI VISTA SUPERIORE:
**Maria Flavia MAMMANA** - LABORATORIO DI MATEMATICHE ELEMENTARI:
**Maria Flavia MAMMANA**

**Credit Value:**12

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

**Taught classes:**70 hours

**Exercise:**24 hours

**Term / Semester:**1° and 2°

## Learning Objectives

**MATEMATICHE ELEMENTARI DA UN PUNTO DI VISTA SUPERIORE**The main objective of the course is to provide students with conceptual and operational tools that stimulate their critical learning towards the Fundamentals of mathematics, with particular reference to the development of geometry. In particular, we intend to offer students a reflection on some conceptual and content nodes that have led mathematicians from the study of the postulated V, to the birth of non-Euclidean geometries.

In particular, the course has the following objectives:

Knowledge and understanding: To know the fundamental aspects of the criticism of the postulated V and the subsequent development of different theories.

Applying knowledge and understanding: Apply the empirical and then scientific method to different mathematical results

Making judgments: Make judgments about the quality of the proposed solution and evaluate its effectiveness. Acquiring critical skills in the areas of mathematics.

Communication skills : Ability to communicate their mathematical knowledge.

Learning skills : Using the knowledge gained to acquire new knowledge.

**LABORATORIO DI MATEMATICHE ELEMENTARI**The aim of the course is to "manipulate mathematics" through DGS, mathematical machines and 3D printing.

In particular, the course proposes the following objectives:

Knowledge and understanding: To know the fundamental aspects of the technologies used in teaching/learning mathematics.

Applying knowledge and understanding: Apply modeling skills in different contexts

Making judgments: Make judgments about the quality of the proposed solution and evaluate its effectiveness. Acquiring critical skills in the areas of mathematics.

Communication skills : Ability to communicate their mathematical knowledge.

Learning skills : Using the knowledge gained to acquire new knowledge.

## Course Structure

**MATEMATICHE ELEMENTARI DA UN PUNTO DI VISTA SUPERIORE**The course will take place tuwice a week. An active participation of the students is required: the lessons will be frontal and participated.

**LABORATORIO DI MATEMATICHE ELEMENTARI**The course will take place tuwice a week. An active participation of the students is required: the lessons will be frontal and participated.

## Detailed Course Content

**MATEMATICHE ELEMENTARI DA UN PUNTO DI VISTA SUPERIORE**Euclidean geometry. Critics for the postulated V. Domostration attempts of the postulated V. The role of Saccheri in the development of non-Euclidean geometries. Non-Euclidean Geometries. Archimedes: the method and its works. Monographic course: Elements of Euclid: book XII

**LABORATORIO DI MATEMATICHE ELEMENTARI**Mathematical machines.

3d printing

regularity in geometric configurations

## Textbook Information

**MATEMATICHE ELEMENTARI DA UN PUNTO DI VISTA SUPERIORE**Attilio Frajese e Lamberto Maccioni (a cura di), Gli Elementi di Euclide, UTET, Torino 1970

M. Kline, Storia del pensiero matematico, Vol.1 e 2. Einaudi, 1999

Evandro Agazzi, Dario Palladino. Le geometrie non euclidee e i fondamenti della geometria.La scuola, 1998

Bruno D'Amore, Silvia Sbaragli. La matematica e la sua storia. Dedalo, 2017

Silvia Benvenuti. Geometrie non euclidee. Alpha test, 2008

**LABORATORIO DI MATEMATICHE ELEMENTARI**Paul Yiu, Notes on Euclidean Geometry, 1998. http://math.fau.edu/Yiu/EuclideanGeometryNotes.pdf

Paul Yiu, Introduction to the Geometry of the Triangle, 2001-2013, http://math.fau.edu/Yiu/YIUIntroductionToTriangleGeometry130411.pdf

Bartolini Bussi, Maria G., Maschietto, Michela. Macchine matematiche: Dalla storia alla scuola. Convergenze, 2006