Università Roma Tre

• Euclidean Geometry: triangles centers, circle inversion.
• Ordered Geometry and Sylvester problem.
• Projective Geometry: axioms, Desargues, collineations and
correlations
• Platonic Solids Euler formula. Politops, 4-dimensional space politops.
• Topology of surfaces and graphs 4 colors problem and 6 colors theorem, Heawood theorem.
• Delaunay triangulations.
• Plane curves, local study of singularities, Newton polygons .

1) H.S.M. Coxeter Introduction to geometry, Wiley 1970;
2) G. Fisher Plane algebraic curves, AMS Students Mathematical Library V.
15, AMS 2001.
moreover
3) M. Aigner, G. Ziegler, Proofs from THE BOOK, Springer, 1998;
4) S. Rebay, Tecniche di Generazione di Griglia per il Calcolo Scientifico-Triangolazione di Delaunay, slides Univ. Studi di Brescia;
5) B. Sturmfels, Polynomial equations and convex polytopes, American Mathematical Monthly 105 (1998) 907-922.
6) Shuhong Gao, Absolute Irreducibility of Polynomials via Newton Polytopes, J. of Algebra