To construct the floor of our bathroom we have only square tiles all equal to each other. We have to put 4 tiles around each vertex in order to cover the whole plane and what we get is an example of a regular tessellation. Another example? Think at the hexagonal cells of the bees. Can you imagine a world where you can combine the square tiles in groups of five around a vertex or the cells of bees in groups of four and remain regular hexagons? Even if it seems strange, by changing some “rules of the game” and some basic concepts of geometry, it is possible and the result is amazing. However we have to clarify what changes we have made; these make us discover the world of hyperbolic geometry. To play with this geometry we usually use a model called Poincaré disk, wherein the “straight lines” take the form of circular arcs and segments. It is possible to discover some properties of these “lines” which are called geodesic on the Poincaré disk and on other surfaces, among which the Beltrami’s pseudosphere. Using multimedial exhibits, one can build regular hyperbolic tessellations and admire the remarkable visual impact they give. The artist M.C. Escher was inspired by this geometry for some of his works. “

“Round … Lines?!” is an interactive exhibition that aims to tell, through a guided tour, the world of hyperbolic geometry, paying particular attention to the tessellations of the hyperbolic plane, which act as a common topic that will guide visitors through the discovery of this unusual and unexpected geometry.