Exploring Expo Geometric Exploits

International world fairs are temporary events in which world countries show themselves in a relative narrow space, in buildings constructed on purpose, usually following the main theme of the exposition. These temporary buildings, by their very ephemeral essence, transient, of rapid construction and consumption, express summarily the image of the historical present through a representation of progress and modernity, using the geometry as a means of symbolic abstraction and as materialization of "aesthetic" choices. The different nations participate to the world fairs in order to show their best characteristics, often coinciding with the achievements in the various fields of knowledge, by giving to the architects the task of representing that with amazing pavilions, exploits of imagery and manufacturing competency. From time to time, those buildings became urban icons. Starting from an historical introduction of some of the most famous and relevant, from a geometric point of view, pavilions, we explore the last world’s fair architecture. Expo 2015 was held in Milan, Italy, from May 1st to October 31st, 2015, and its main theme was Feeding the Planet, Energy for Life. Although it is noticeable, in this expo just ended, that geometries represent mainly the configuration of the exteriors, some pavilions occur anyway as objects for which the search for the form is addressed starting from strong geometric figures. It may be noted that in some cases the volumes and in others the surfaces determine the external images of the pavilions and in some cases also the character of the interior. Examining the world fairs from their beginning we notice that the temporary nature of these events offer limits but also freedom to experiment with buildings, very often using a geometric inspiration as materialization of "aesthetic" choices. We see infact how geometry/math is important in the exemplified cases, and from different points of view (inspiration, design, building techniques, digital management of the construction etc.). The projects follow, as in the case of Philips pavilion, new geometries, new technologies (hyperbolic geometry in buildings was at that time on the rise, thanks to the new systems of construction) or, in the case of Italia Pavilion, the possibility offered by math tools (BIM) as well as new materials. We have examined only some of the pavilions, further studies will be published in a book, exploring all the geometric exploits of this edition of the world fairs.