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 will explore the last world fair architecture. Expo 2015 was held in Milan, Italy, from May 1~(st) to October 31~(st), 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. We will examine only some of the pavilions - it would occur a book to deal with all - exploring the geometric exploits of this edition of the world fairs.
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