Nexus Network Journal

The threefold interest in architecture, biology and mathematics motivated us to examine and justify new architectural forms. We discuss some notions of rhythm: Euclidean, morphogenetic and morphologic. Contemporary relationships between structure and form are based on the generation of shape by technological processes, thus the resulting objects are restricted to their material expression. Here a phenomenological organisation of form and its continuity with the landscape arise out of the mathematical and architectural creativity. The use of the computer is applied from outside to inside instead from inside to outside; this means that we are dealing with the organisational processes via continuous methods instead of evolutionary processes given by computer simulations, known as genetic algorithms, where the resulting configurations are reduced to a matter of routine. The role of design as an aesthetic component innovates the theoretical framework of structural engineering to establish the architectural environments.

The main goal of this study is to apply a scientific quantitative approach to the investigation of contextual fit. This is approached mathematically within the framework of cognitive science and research on categorization and prototypes. Two experiments investigated two leading mathematical-cognitive approaches for explaining people’s judgment of contextual fit of a new building with an architectural/urban context: prototype approach and feature frequency approach. The basic concept is that people represent the built environment via architectural prototypes and/or frequencies of encountered architectural features. In the first experiment, a group of twelve participants performed rank order tasks on artificially created architectural patterns, for the purpose of psychological scaling. Perceptual distances among all patterns were mathematically determined. In the second experiment, three groups of architectural patterns were constructed to represent assumed architectural contexts. The prototype of each context was mathematically determined according to prototype cognitive model, and based on the distances calculated in the first experiment. Fifty-six students participated in the main experiment, in which they rank ordered a group of fifteen architectural patterns in terms of contextual fit to each of the three architectural contexts. Participants’ rank order data of the fifteen patterns were regressed on both the perceptual distances from prototypes, and numbers of features shared with each architectural context. Results indicated that both prototype and feature frequency approaches significantly accounted for important portions of participants’ judgments. However, participants tended to prefer one approach to the other according to context composition. Results have implications for both research on utilizing cognitive-mathematical models in architectural research and on urban design guidelines and control.

Nicola Zabaglia, master mason of the Fabbrica of St. Peter’s and inventor of many ingenious mechanical devices for restoration, was also the director of the “School of Practical Mechanics” for the education of young labourers. At a time when traditional operational experience was strongly rivalled by the coeval achievements in the theory of mechanics and its effect on building, the work of Zabaglia became an instrument of propaganda. Since empirical practice and the oral transmission of operational knowledge were called into question by the pressing progress of science as well as by new institutions, the works of Zabaglia and his talented students were not only an influential model of cohesion between architecture, building yard and applied mechanics, but also a melancholy epilogue of a practical tradition inexorably condemned to oblivion.

This paper presents an examination of the process of the development of module in the works and theories of Japanese architect Ikebe Kiyoshi (1920–79). Ikebe based his idea of module on the belief that “Beauty is Mathematics” He applied his ideas of module in various ways from the 1940s to the 1970s. Analyzing his ideas and works against their historical background, the social and creative meanings of the idea of module and of mathematics in architecture will be re-examined. This allows us to see how Ikebe developed his ideas of module from a characteristic mathematical approach, and how he developed his idea of mathematical logic into his creative theories based on the flexible nature of people’s lifestyles and social conditions. Going beyond the cultural and social differences and the limitations of Le Corbusier’s Modulor, the idea of module as the method for organizing human space in a harmonious manner was reframed in Ikebe’s works, and was developed in a more flexible mathematical way.

The present work is a limited analysis of the traditional urban fabric of Muslim cities in the light of this theory. Chaos theory provides better instruments for the analysis and understanding of the traditional urban fabric in old Muslim cities that have, paradoxically, long been considered as lacking order and thus “chaotic” in the pejorative sense! Beyond the analysis, our study also aims at providing a fresh approach to the built environment that shifts the architectural and planning professions from the traditional design and planning approach to a self-generating process that, once set up, would function and develop without need for intervention. However, the present study will be limited to the application of such concepts at two levels. At the urban level, it will provide evidence of the existence of chaos and fractals at the scale of the city. At the domestic level, concepts are applied to housing evolution and community spaces.

In this brief note the authors describe the studies undertaken to date regarding the dome of the Basilica of San Gaudenzio in Novara designed by Alessandro Antonelli, with particular emphasis on the geometry and statics of the external dome. Following a brief summary of the events and vicissitudes attendant on the construction of the dome, the structure will be examined from the point of view of the geometry, the construction techniques, and the materials used, in order to clarify the static behaviour and the stability of the whole set of structural and constructive elements of which the dome is composed. These studies have allowed us to obtain the necessary information for evaluating the complex and ambitious structural achievement of a significant element of Antonelli’s basilica.

This paper is one of a set of lessons prepared for the course of “Theory of Architecture” (Faculty of Architecture — “La Sapienza” University of Rome). The didactic aim was to present — to students attending the first year of courses — some methods for the beginning stages of design and their applicability to any kind creative work. The brief multimedia hypertext quoted at the end of this paper was carried out in collaboration with the “LaMA” (Laboratorio Multimediale di Architettura) as a test for new educational tools applied to first our “e-learning” experiences.

The complexity shown by some geometrical patterns of Roman mosaics and the high quality of their realization lead to think that for such patterns, unlike scenes with human or animal figures, a model of the general pattern was certainly not sufficient to guide the setting up; in order to answer this question one is led to conjecture the existence of diagrams (key diagrams) with which the craftsman, by looking at them, is able to identify (and/or remember) the geometrical structure of a basic element of the general pattern, as well as a way for constructing it — and possibly the whole pavement — with his usual instruments. This hypothesis is applied to some patterns which were well spread over the Roman world. The present study aims at showing how a given key diagram can apply to varied patterns and, conversely, how the making of a given complex pattern can rely on several articulated key diagrams.

This paper discusses the discovery that four oblique prisms with a square cross section can intersect, forming a joint by means of a notch parallel to the horizontal plane. The use of this joint in new constructions is explored.

The aim of this paper is to show how efficient mathematical models can be in simulating situations that are apparently distant from one another. The works of M. C. Escher and Buckminster Fuller are used as starting points for the exploration of the first applications of non-Euclidean geometry to architecture. The investigation goes on to fractals and chaos, nurbs, blob architecture and deconstructivism.