The concept of beauty in architecture takes on many meanings in relation to the issues to which it relates, since ancient times we have been questioning ourselves in an attempt to identify the formula to satisfy the aesthetic and functional requirements of the harmony of forms.

The three parameters exposed by Vitruvius firmitas_ utilitas_ venustas remain the key concepts around which the enigma of architectural beauty revolves, to be connected to the historical and cultural moment they relate to.

The complex prerogative of satisfying the senses through aesthetic configurations that overcome the uncertainty inherent in subjective judgment, generates a series of bonds that associate the idea of beauty with that of well-being, functionality, order, harmony, proportion.

The search for an ideal aesthetic has therefore directed towards rational formulas capable of scientifically expressing beauty. In this sense, the mathematical concept of proportion has influenced the architects of the past, in the search for the most suitable geometric relationships many of them have assigned a fundamental role to the golden section . The numerical relationship also expressed a mystical and philosophical meaning, it was measure and religion, as specified by Luca Pacioli who in 1509 dedicated an entire treatise to him in De Divina Proportione , in which he describes its rules and effects.

As is well known, in the Renaissance the rules derived from antiquity are theorized in their relationship with the human body from which symmetries, proportions, comparisons and various aesthetic symbioses with architecture are generated. The arithmetic, geometric and harmonic correspondences also base the theories adopted by Andrea Palladio to establish the dimensions that determine the shape of the rooms. Similarly Leon Batista Alberti examines the correspondences between musical intervals and architectural proportions.

The search for universal harmony is filtered through Neoplatonic thought and Christian doctrines that also regulate the shape of cities, based on modules and geometries from which the layouts are derived and from which the design of perfect architecture arises. The result is an architectural lexicon centered on order, on a eurythmic system that makes up the various parts of the work.

Proceeding in the twentieth century the avant-garde movements resume the studies on proportions and the idealization of geometry, Jacques Villon in 1911 founded the Section d'or movement, in the same vein the work of Gino Severini arises who, trying to rediscover the meaning that the Greeks had given to number and geometry , elaborates a real aesthetic of number and compass.

The intrinsic beauty in numerical ratios was also sought by artists belonging to the DeStijl , such as Oscar Schlemmer who, in the context of the Bauhaus, analyzes the decomposition of the human body based on the golden ratio, a proportion further developed by Le Corbusier for the Modulor , consisting of two series of Fibonacci interrelated with each other.

Starting from the 1930s, Luigi Moretti introduced the concept of parametric architecture with the aim of formulating a new, truly modern architectural language capable of going beyond the schematisms and the state of academia in which it continued to remain. He therefore tries to overcome the limits of "rationalism" which in his opinion had given summary answers, addressing the issues of architectural renewal on a purely formal level, thus proposing the scientific concept of beauty based on mathematical criteria , deriving in this case from the interrelationships between form and function.

The brilliant architect flanked by the mathematician Bruno De Finetti and by experts from different sectors, engineers, biologists, psychologists, economists capable of facing the problems related to the complexities of the modern city, tries to define a design method based on objective rules, capable of translating fit needs and functions.

The articulation of the spaces, in this way, would not derive from taste, from "personal vanity", from the individual choices of the designer, but from the impartial development of the complex functions that define an architectural structure calculated through computers that obtained variations of the forms when changing parameters.

Moretti's surprising anticipations, not brought to fruition due to the lack of processors capable of managing the enormous amount of data, configured an ideal of beauty oriented towards contemporaneity that invite us to reflect on the appropriateness and current meanings of the term, on overcoming exclusive of the aesthetic dimension.

Trying to conclude the difficult topic with some fixed points and still many questions, the concept of beauty in architecture cannot be separated from the already described connections that have always belonged to it, plus the problems of today's society are added: the answers to the social question relating to urban quality, peripheral areas, abandoned spaces, environmental risk, mobility, ecologically sustainable building production, in synthesis of the ethical and aesthetic qualities that concern the spaces and configurations of everyday life.