Course unit content
<br />The Babylonian and Egyptian mathematics.<br />The Greek mathematics: Thales, Pythagoras and his school, the crisis of incommensurables. Zeno’s paradoxes.<br />The three famous problems of Greek antiquity: quadrature of the circle, duplication of the cube, trisection of angle. Hippocrates and the quadrature of lunula.<br />Plato: arithmetic and geometry, the platonics polyedra.<br />Numerics systems: natural, integer, rational, real, complex numbers. The fundamental theorem of Algebra.<br />Numbers p, e, j. <br />Non-Euclidean geometries: hystorical and epistemological aspects, Poincaré’s and Klein’s models.<br />The Erlangen program and the transformations geometry: congruence, similarity, affinity, projectivity. <br />The geometrical transformations in Escher’s works.<br />The geometrical transformations in the space.<br />The problem of foundations of Geometry: the Hilbert’s axioms, indipendence, coherence, completeness.<br />