Located in the commune of Oued Yaich in the wilaya of Blida (Algeria), the "Sâad Dahlab" University was designed at the end of the 20th century by the American agency S.O.M (Skidmore, Owing & Merrill), while the Structuralist movement tended to assert itself throughout the world. Following its independence in 1962, the country underwent a major reconstruction phase that opened up a new field of experimentation for many architectural agencies and offices (Chaulet & chaulet, n.d.). Walter Andrew Netsch, the architect in charge of the project, was recognized for his groundbreaking Field Theory design method in the mid-20th century.

The latter is based on a combinatorial process that, from a basic pattern resulting from the superposition of a square and a square oriented at 45°, allows to generate an infinity of geometric grids, extensible to infinity. (Jones, 1990-05-01) The architectural composition of a building is based on these frames, which provide a continuous and homogeneous proportion system that can be expanded infinitely. Aiming to schedule an architectural design and allowing it, in theory, to evolve and adapt over time, the approach developed by Netsch seems to join the thought of the Structuralist movement of which it incorporates some major notions: "growth", "articulation of the built mass" and "the part and the whole" (Luchinger, 1981).

The Blida university's conception in Algeria was based on geometric and mathematical laws that govern the various parts and the whole (Netsch, 1980-05-04). In light of this observation, it is essential to question the geometric transformations and mathematical relations that enabled the campus plans to be created. This article attempts to identify the mathematical foundations that lead to the forms of “Saâd Dahlab” University of Blida. The primary objective is thus to highlight the laws (field) that made it possible to generate the various plans, namely the mass plan of the university, the plan of pavilion 26 and the structure of an architectural unit (earthenware tile), and to understand the process by which the Theory of Fields was applied. (See Figure 1)

Admitting that having been designed by the architect Walter Netsch, the University of Blida, presents the application of several principles relating to structuralism and starting from the postulate that the basic pattern, at the origin of the field and managing the structure of the ground plane (infinite growth mesh), from the building to the earthenware tile, is the combination of a square and its rotation at 45°, the work developed in this essay is a qualitative study by experimentation, based essentially on a geometric analysis of the different planes (Blum, 1997).

The University of Blida was conceived in Algeria following this same modus operandi, a series of questions arose from which we then discovered our general problematic.

Thus, our issue is articulated through two main questions:

1. What are the mathematical principles that underlie the structures of “Saâd Dahlab” of Blida University?

2. What were the methods employed to incorporate the architectural characteristics of the Casbah of Algiers into the project's design principles?

The main objectives of our study are:

The Field Theory approach to architectural design is based on a complex combinatorial process that typically begins with a basic geometric figure like the square. The basic pattern is created by superimposing a square and one that is oriented at 45°, starting with this regular quadrangle. The pattern obtained is then repeated indefinitely according to various axes and directions. The creation of a grid from the same basic unit can be done in this new geometric game, which is regulated by measurement reports (Massu, 1997). The architect defines moiré patterns by overlapping two or more grids. As follows: "A lattice is when you rotate a sheet that has these forms and then you put another sheet over and you draw it all over again. In fact, you draw it a third time". (Bruegmann et al., 2008).

The final step is to superimpose the obtained mesh network on the first sketch of the project. The mesh's continuous and homogeneous proportion system enables the establishment of relationships between the parts of the plan and the whole. This conceptual approach ensures dimensional consistency at different scales, between different buildings, and between different elements of the building thanks to the multiplication or division of the initial module (S.O.M., 2015) & (S.O.M., 2016). (See Figure 2).

In addition, we incorporated a theoretical framework based on the Fibonacci digital system, which was explored and developed in Algerian projects by architect Walter Netsch. We identified a basic pattern from various geometric manipulations, surrounding the Fibonacci suite, using a grid published by SOM on an internet platform.

Fibonacci series is a theoretical field that relies on the mathematical system of Fibonacci (1, 2, 3, 5, 8, 13, 21, 34, etc.) and has numerous variations. The system is currently being explored for projects in Algeria where Fibonacci developed his mathematical system." (S.O.M., 2016).

From a unitary central square, it is then possible to draw a first grid, following the growth system of the suite, and which will serve as a support for the initiation of a first spiral of Fibonacci – a spiral approaching the golden spiral. Three repetitions of the process were made with successive rotations at 90° around the same unit quadrilateral, which resulted in the formation of the pattern's distinctive helical structure. The four primers obtained in turn define a second square, tangent to the different vertices generated by the curvature of the spirals and whose side is equal to three times the side of the central square, then a third square, rotated at 45° and determined by the extension and intersection of the propeller arms. Different lines and segments, including diagonals and mediators, are used to form the divisions and subdivisions of the four main quadrilaterals and form the remaining details of the pattern. (See Figure 6).

It is possible to identify many analogies by superimposing the resulting pattern and adapting it to the plan of one of the original three faculties. Firstly, the unitary (or central) square of the pattern defines the inner courtyard, which is the core of the building. Second, the main square of the pattern delimits the frame of the main structural grid of the pavilion (that of 7.5 x 7.5m), extended to include the basic triangles intended to accommodate the service spaces. The primers of the four propellers, forming the square oriented at 45° of the patterns, define the hypotenuse of one triangle on two and thus determine the inclination of the elements in front integrating the vertical circulation. Finally, the main divisions of the grid pattern (diagonal and median) define the elements and supports on which the fundamental geometric manipulations to compose the pavilions are based. The diagonals and mediators represent the axes that divide the building into four blocks and determine the center and angle for generating them from a first.

The pattern thus repeated makes it possible to generate different pavilions and pathways connecting them. The University of Blida 1 Saâd Dahlab seems well underpinned by a structure ensuring the coherence of the whole and articulating the parts and the whole. The institution develops at different scales according to the same scheme, similar to fractals, with the aim of creating various subsets based on a logic that involves organizing spaces around a central core. (See Figure 7)

Walter Netsch has profoundly impacted modern architecture with his groundbreaking design methodology, termed Field Theory. His significant designs encompass the University of Illinois at Chicago (UIC) Campus (1965), where he emphasised functional clusters of buildings that facilitate user interaction. The University of Illinois at Chicago (UIC) campus design by Walter Netsch was influenced by early Greek and Gothic buildings as well as the DNA double helix. The Behavioural Science Building, Science and Engineering South, and Architecture and Design Studios Building were among the first designs, with elaborate floor plans. Netsch changed the campus's layout in spite of early criticism in order to improve accessibility and usage while addressing difficulties with upkeep and inadequate finance.

Walter Netsch's designs for the University of Illinois at Chicago (UIC) campus and Blida Campus University in Algeria are testament to his Field Theory architectural approach. Netsch's dedication to community engagement and geometric complexity is evident in the designs of these campuses, which incorporate his innovative geometric principles. The UIC campus, which is influenced by DNA patterns and early Greek and Gothic architecture, endeavours to cultivate a sense of community and intellectual exchange through complex building arrangements.

On the other hand, the Blida Campus University likely implemented comparable geometric principles to establish a cohesive educational environment that is responsive to its cultural and landscape context. The campus boasts a series of squares that have been rotated, resulting in floor plans that resemble a labyrinth, which promotes interaction and exploration. Critics initially refer to it as "Fortress Illini" because of its elevated walkways and imposing structures. However, the design likely includes open spaces and concentrations of buildings that encourage interaction and movement, like it's was conceived in Blida university.

The effectiveness of this integration would be contingent upon the extent to which the campus promotes accessibility and engagement with its surroundings.

In general, Netsch's Field Theory approach in these two comparative cases underscores his adaptability as an architect and the significance of addressing local environments while pursing innovative architectural solutions.

The application of field theory at the University of Blida is characterized by many characteristics, just like the projects designed by Walter Netsch. Each discipline set has a continuous and homogenous dimensional structure that allows for control over the internal dimensions of each pavilion and the articulation of different units between them. By adding identical modules, Blida University's plan is structured in a similar way to structuralist theory structures. Blida University places a strong focus on geometric order and mathematical rigor. Blida University has a framework that underpins every aspect, from the ground plan to the decor elements, and the configuration of the institutes. A system of proportions is provided to ensure that the parts and the whole are coherent. (See Figure 8).

Teaching faculties are configured using an additive and modular process. The central building's core is formed by the arrangement of the different spaces, with a quadrangular inner courtyard being the first module. A radioconcentric scheme is used to multiply the obtained unit into a second module, which generates the paths and entities that host the various Institutes. The module portions are determined by the program's requirements. At different levels, it appears that the lines at the bottom of the plans are the result of a clever geometric arrangement between the square, the square oriented at 45°, and the circle. These elementary figures become complex compositions when combined using various scale ratios, which are primarily based on three numerical systems of proportion, namely the Fibonacci suite, 2 and 5.

Lastly, it can be observed that the project does, in fact, draw inspiration from the geometric tradition and richness of forms and materials found in Muslim culture. A number of elements are used that tend to evoke the unique characteristics of the architecture of the Casbah of Algiers (Missoum, 2003) & (A, 1989), such as the pavilions' introverted configuration, the helical scheme's application in the composition of plans and decorations, and the hierarchy of outdoor spaces.

The abstract of this paper was presented at the Cities’ Identity Through Architecture & Arts (CITAA) Conference—8th Edition, which was held on the 17^th – 19^th of September 2024.