Horizons in Biblical Theology

A laser-assisted survey was undertaken in 2022 at Palladio’s Redentore in Venice. Calculating the proportional relationships between the significant interior dimensions made it possible to suggest a sequence of steps by which Palladio could have developed his design for the whole church. The total interior length and the transept width were determined by the available site; they were likely the basis from which the other dimensions of the church plan were generated, by using a series of interconnected proportional ratios. The plan dimensions could have determined the vertical dimensions of the elevation. The width/length/height relationships conform to Palladio’s methods to determine the height of vaulted rooms. The study found significant evidence that Palladio was influenced equally by the prescriptions of Alberti and Vitruvius, and the design procedures of traditional medieval building. The design sequence suggested here provides a more thorough explanation of the design process at the Redentore than any hitherto proposed.

Nexus Network Journal: Architecture and Mathematics guest editors Theodoros Dounas and Davide Lombardi introduce Vol. 27 (1). This special issue aims to deepen the understanding of formal methods in architectural composition by exploring three distinct approaches: syntactical (assembling elements), typological (reinterpreting existing archetypes), and computational (applying computational processes to generate form). Each approach incorporates mathematical principles that shape design creation and offer a framework for evaluating and testing architectural compositions. For instance, geometric transformations can be encoded as algorithms or grammatical rules, while parallel analytical processes validate these generated designs.

Abstract The article introduces a novel construction that simplifies the drawing of cubical perspectives. A recent work described a method for drawing cubical perspectives which classifies lines into several types and renders each type systematically. Some of these types require an auxiliary external construction, hindering the drawing process. This research proposes a novel method that shortcuts this step with an internal construction. This method both accelerates and simplifies the studio process, reduces systematic errors, and makes freehand sketching more viable and precise. Next, the shortcut is applied through the case of the Solimene factory (Italy), an organic architecture that highlights both the issues inherent to cubical representation and the advantages of the proposed shortcut.

Abstract We present a novel workflow where non-rectangular floor plans (NRFPs), namely plans with at least one concave corner, are self-generated using a model that directly encodes key optimisation factors on spatial quality and energy consumption, with non-rectangular building envelopes. The modelling considers a number of key factors including architectural and urban quality, net zero factors and adherence to general residents’ feedback from previous studies. We provide evidence that the proposed workflow outperforms a number of optimisation solvers generally used in computational design, in those cases where solar radiation is most needed. Our study combines a syntactic approach with a computational one with a novel workflow to encode tangible and intangible factors to improve a specific class of non-trivial floor plans (L-shaped).

This paper investigates the architectural and structural potential of folded-smooth (F-S) hybrid shell structures, modeled using the Takagi-Landsberg (TL) function and Iterated Function Systems (IFS) to achieve smooth transitions between folded and smooth surfaces. Using a hyperbolic paraboloid (hypar) profile, the study evaluates the distinct structural behaviors of F-S configurations. Finite element analysis shows that lateral F-S shells with folded ends at the ground achieve comparable stability to smooth hypars, while longitudinal F-S shells with unsupported ends show structural weaknesses, particularly at flying edges. Despite construction challenges, the study demonstrates that F-S shells combine structural robustness and aesthetic flexibility, advancing design possibilities in hybrid architectural forms.

Hyperbolic Paraboloids (hypar) are saddle-shaped doubly-ruled surfaces, which combine features of both hyperboloids and paraboloids. The form is commonly used in bamboo architecture as it exploits straight full culm bamboo poles to achieve striking curved roofs. The authors seek to answer a research question related to key steps in generating the form of multi-hypar bamboo structures with roof surface shapes as the primary design parameters. This research was conducted in four stages through full-scale construction, hands-on experiments, case studies analysis and summarised with operational steps. The study is concluded by suggesting four key steps aimed to aid novice designers, which are: creating the roof surface, subdividing it into modules, defining edge lines through composition principles, and generating hypar surfaces. Potential further research includes integrating structural performance assessments and computational techniques for broader applications in bamboo design.

The purpose of the current study was to comprehensively investigate the facades of the Mausoleum of Khoja Akhmet Yasawi, its geometric patterns and the mathematical laws used for their design. To do this, the writings of medieval mathematicians were analysed, and their principles considered to model the geometric patterns of the facades. The paper describes the evolution of geometric laws in the Islamic world from the 7th to the 9th century. The Mausoleum of Khoja Akhmet Yasawi is one of the best examples of geometric architectural applications from the 14th-15th century. The facades of Khoja Akhmet Yasawi seemingly rely on the methods of two mathematicians, Al-Farabi and Al-Khwarizmi. To a greater extent, the ornaments derive from dividing equilateral triangles, parallelograms and polygons to create geometric figures. The façade patterns of the Khoja Akhmet Yasawi complex require careful calculation and preparation due to their conciseness and harmony, giving insight into the fields of arithmetic, geometry and architecture and architects’ education during the 14th-15th century.

First proposed in the 1960s, Conversational Architecture enhances human and computer-integrated built environment interaction. Nowadays, most interactive designs are based on reaction and automation, rarely on conversation. Despite Natural Language Processing, including Large Language Model (LLM), being considered a candidate for Human-Computer Interaction (HCI), LLM applications are limited to verbal communication. The syntactic relationship between LLM, and architectural composition is underexplored. The paper proposes a qualitative framework to integrate the theoretical research of LLM and HCI in Conversational Architecture design. Through a mathematical and algorithmic analysis of a transformer model, the key component of LLM, its attributes are mapped onto Conversational Architecture parameters. With the identified design implications, a theatre hall design experiment is conducted. Through observation, the feasibility and challenges of the proposed framework are analysed.

The funerary structures known as kümbets, developed during the Anatolian Seljuk period (1077–1307), represent a distinctive architectural typology. This study first demonstrates that each Anatolian Seljuk kümbet is unique in its sectional geometry. It then employs statistical methods to analyze these structures, with the aim to understand their architectural styles and formation principles through measurable geometric features. The scope includes the analysis of 56 section drawings of 67 freestanding kümbets. The methodology involves data collection and preparation, feature selection, and dataset refinement using a box plot technique, followed by correlation analysis. Among the 28 correlations analyzed, 18 are statistically significant. One of the strongest correlations indicates a strong inverse relationship between the cap's inner angle and cap height (r = − 0.93), while the weakest is a positive relationship between cap height and interior wall height (r = 0.27).

This paper introduces a computational framework driven by a generative algorithm that allows both architects and non-experts to create various floorplan layouts for predefined residential unit boundaries. This generative tool, implemented in GhPython and Grasshopper, enables users to customize floor plans by defining specific area requirements, accommodating diverse user preferences and facilitate the design process. Also, a catalog of module-based slices containing different functional spaces with determined dimensions have been designed as a reference for the algorithm to generate the final layouts. The generative algorithm, which uses numerical data from each slice, produces floorplan configurations based on the adjacency of functional spaces and user-defined parameters. The bottom-up approach of the algorithm means that the results are noticeably influenced by the designed slices. With the intention of providing the users with a more intuitive understanding of housing layouts, the generated floorplans are presented as furnished 3D models, clustered under specific categories.

The authors present some of the results of the recent survey campaign carried out along the northern section of the city walls of the unearthed city. The paper focuses on the documentation of the site as the starting point of a workflow for analysing the morphological characteristics of the existing cavities. The 3D virtual casts, based on 3D reality-based survey, were obtained through reverse modelling procedures in order to provide useful data for the calculation of the parameters inherent to the terminal ballistics of the weapons used. The peculiar vicissitudes that characterise the excavation of ancient Pompeii exclude the possibility of any contamination by the impact of firearms. This makes the documentation of exceptional value for thinking about neuroballistic weapons, of which only a few damaged artefacts have partially survived. The use of polybolos, which has been hypothesised after careful consideration, confirms the usefulness of an independent space for the elaboration of original and transversal thoughts, guided by the collection of data and oriented by their graphic visualisation.

Deployable structures, with ability to transform, open possibilities for creating adaptable spaces by balancing aesthetics with structural integrity. A crucial challenge lies in understanding expandability, the feasible range of opening. This study addresses this by developing a computational method that analyzes the geometry and structural performance of deployable bamboo structures. This method automatically generates geometry and analyzes expandability. It investigates how shape and size influence expandability, informing designers early in the design process. The findings reveal that bamboo diameter and layer count significantly impact expandability, while depth and the number of scissors-like elements have minimal effect. Then, designers can navigate the design space with confidence. This study advances the understanding of the expandability so architects can explore feasible designs early on and thereby push the boundaries of architectural composition.

This letter from the editor introduces Vol. 26(4) of the Nexus Network Journal: Architecture and Mathematics. This issue features research that measures, analyses, and scripts architectural forms and elements to reveal insights into celebrated examples and propose novel methods for generating buildings or components. Geographically, the research in this issue includes detailed examinations of historical buildings in China, Greece, Iran, Spain and the United Kingdom. The building types explored range from railway stations to religious structures and military facilities. The methods include surveys, generative scripting and deep learning models.