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Geometry
The first two years will have as its objective the knowledge of the fundamentals of Euclidean geometry
piano. The importance and meaning of the concepts of postulate, axiom, definition,
theorem, demonstration, with particular regard to the fact that, starting from the Elements of
Euclid, they permeated the development of Western mathematics. Consistent with the
way in which it has been presented historically, the Euclidean approach will not be reduced to one
purely axiomatic formulation.
Particular attention will be paid to the Pythagorean theorem so that both are understood
the geometric aspects and the implications in number theory (introduction of numbers
irrational) insisting above all on the conceptual aspects.
The student will acquire knowledge of the main geometric transformations (translations,
rotations, symmetries, similarities with particular regard to Thales’ theory) and will be able
to recognize the main invariant properties.
The creation of elementary geometric constructions will be carried out using tools traditional (in particular the straightedge and compass, underlining the historical significance of this methodology in Euclidean geometry), and through geometry computer programs. The student will learn to use the Cartesian coordinate method, in a first phase limited to the representation of points and lines in the plane and properties such as parallelism and perpendicularity. The intervention of algebra in the representation of geometric objects will not be separated from the deepening of the conceptual and technical scope of this branch of mathematics.