Some important results about art gallery theorems are proposed, starting from Chvátal’s essay, using also polygon triangulations and orthogonal polygons.

In this paper I consider some data of Covid-19 infection in Italy from the 20th of February to the 29th of June 2020. Data are analyzed using some fits based on mathematical models. This analysis may be proposed to students of the last class of the Liceo Scientifico in order to debate a real problem with mathematical tools.

In this paper the author presents a new form of hexagon and the solution of the open problem of classifying plane hexagons. In particular are illustrated the forms of crossed and simple n -gons for n = 3, 4, 5, 6 and also the forms of simple ones for n = 7, 8, 9. A graphic way to construct new forms of polygons is illustrated.