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.
• Newton polygons .
• Introduction to tropical geometry.

1) H.S.M Coxeter Introduction to geometry, Wiley 1970; + appunti.

selected pages from

2) D. Hilbert, S. Cohn Vossen, Geometria intuitiva, cap. 3 , 1932, ed. varie;
3) M. Aigner, Martin, G. Ziegler, Proofs from THE BOOK, Springer, 1998;
4) J. Stillwell The Four Pillars of Geometry, Springer 2005;
5) H.D. Ebbinghaus, H. Hermes, F. Hirzebruch, et al. Numbers, GTM 123, Springer 1990;
6) Stefano Rebay, Tecniche di Generazione di Griglia per il Calcolo Scientico-Triangolazione di Delaunay, slides Univ. Studi di Brescia;
7) G. Fisher Plane algebraic curves, AMS Students Mathematical Library V. 15, AMS 2001.
8) H. Rademacher, O. Toeplitz The enjoyment of mathematics, Princeton Univ. Press, 1957 (e ristampe) .
9) B. Sturmfels, Polynomial equations and convex polytopes, American Mathematical Monthly 105 (1998) 907-922.
10) Shuhong Gao, Absolute Irreducibility of Polynomials via Newton Polytopes, J. of Algebra 237 (2001), 501-520.
11) D. Speyer and B. Sturmfels, Tropical mathematics, Mathematics Magazine 82 (2009) 163—173;
12) G.Mikhalkin Tropical geometry and its applications. International Congress of Mathematicians. Vol. II, 827–852, Eur. Math. Soc., Zürich, 2006
13) E. Brugallé, Erwan;I. Itemberg, G.Mikhalkin, K. Shaw, Brief introduction to tropical geometry. Proceedings of the Gökova Geometry-Topology Conference 2014, 1–75, Gökova Geometry/Topology Conference (GGT), Gökova, 2015