Teaching - Università Roma Tre

ME420 - FOUNDATIONS AND HISTORY OF GEOMETRY (objectives)

Code

20410618

Language

ITA

Type of certificate

Profit certificate

Credits

6

Scientific Disciplinary Sector Code

MAT/03

Contact Hours

48

Exercise Hours

12

Type of Activity

Core compulsory activities

Teacher	CAPORASO LUCIA (syllabus) 1 Euclid's Geometry. Ruler and Compass Constructions Euclid's Axiomatic Method. Construction of the Regular Pentagon. Newer results: The Euler line, the nine- points circle, the orthic triangle. 2 Hilbert's Axioms Axioms of Incidence Axioms of Betweenness Axioms of Congruence for Line Segments Axioms of Congruence for Angles Hilbert Planes and Existence of isosceles triangles Intersection of Lines and Circles Euclidean Planes Archimedes' axiom and Dedekind's axiom 3. Geometry over Fields The Real Cartesian plane Abstract Fields and Incidence Pappus’s thorem Ordered Fields and Betweenness Congruence of Segments Archimedes' axiom and Dedekind's axiom for fields Rigid Motions and SAS Pythagorean and Euclidean fields Non-Archimedean Geometry Construction Problems and Field Extensions Constructible numbers Duplication of the cube. Trisection of the Angle Squaring of the circle Constructible polygons and Fermat’s primes 5 Non Euclidean geometry Circular Inversion Poincaré model (reference books) Robin Hartshorne. Geometry: Euclid and beyond. Springer-Verlag, New York-Heidelberg.
Dates of beginning and end of teaching activities	From to
Delivery mode	Traditional
Attendance	not mandatory
Evaluation methods	Oral exam