The geometry (science of the form and the space) and the architecture they possess an interesting road along the history of the western thought. The geometry contributes its capacity to interpret the structuring of the world and of the reason; while the architecture contributes with its capacity to transform the semantic and physical aspects of our habitat. The different advances in the geometric representation have defined the characteristics of the architectural spaces that go: since the rigorousness modulating of the Classicism and the birth of the Euclidean geometry, to the contemporary informalism; the incorporation of the digital mathematical calculation, and its strong review of the traditional cartesian space.