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.

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

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

Learning assessment may also be carried out on line, should the conditions require it.

The mathematics of the ancient Egyptians. Mathematics in the classical period: the Greek schools. Euclidean geometry. Criticism of the V postulate. Attempts to demonstration of the V postulate. The role of Saccheri in the development of non-Euclidean geometry. Non-Euclidean Geometries. Archimedes: the method and his works.

Deepening: the "Grundlagen der Geometrie" by Hilbert; axioms of continuity and non-archimedean geometry.

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