New technologies are based on complex algorithms which, by the use of simulators, achieve to produce complexity works that would have been unbelievable twenty year ago. These algorithms have a strong mathematical basis and allow to generate other working methods so as to create wonderful geometrical objects. The study of this New Geometry requires to explore and expand this field of knowledge in the Architecture studies. In order to analyze and use complex design systems to generate non linear experimental models, it is necessary the Mathematical contribution, not only at the University education stage but also at the professional life.

This New Mathematics adequately focused, is able and must be an essential ally to creative design which is born with an exercised imagination in the formation stage; therefore it must aid to establish a space where knowledge and ability for architectural work can be created, synthesized and experimented.

This work tries to encourage students and in relation to Geometry promotes the following aspects: (i) Inspection of new architectural spaces, (ii)Comprehension of the geometrical structure, (iii) Originality and common sense, (iv) Relation between Geometry and design of construction constitutive elements,(v) Insertion of man in the space, (vi) Conditioning of design to human body dimensions, (vii) Fractal geometries.

According to what has been expressed, this proposition acquires a fundamental significance to develop a spatial vision of geometrical shapes in students, in order to stimulate the understanding of the existing relation between abstract geometrical elements and their real applications in Architecture, Geometry and Design and Art. Besides, the purpose of this work has the aim to approach knowledge at the architectural design process and to the study of shapes and mathematical models that such designs sustain , and ultimately demonstrate the importance of an academic organization that involve teachers from different disciplines.