Drawing with Numbers: Geometry and Numeracy in Early Modern Architectural Design

Carpo, Mario

doi:10.2307/3592497

Cited by 40 publications

(12 citation statements)

References 12 publications

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“…It was already used to control the formal development of the spiers on the Gothic facades and the complex operations of the stereotomy of Northern cathedrals [16], and it is no coincidence that it explicitly appears in a drawing of fortifications by Albrecht Dürer [17]. In addition to this graphic convention, there is also the habit, always in the treatises, of using the horizontal section of the column to visually show the relationship in modules between the base and the height, a visual alternative to the Albertian numerical fractions [18].…”

Section: From Drawing To Buildingmentioning

confidence: 99%

Borromini, the Casa dei Filippini and the Two-Way Relationship between Representation and Architectural Form

Colonnese,

Carpiceci

2023

Architecture

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The stratified relationship and mutual influence between the representation of the project and the form of built architecture manifest above all in the facade design by virtue of its natural rhetorical vocation. This is the case of the Casa dei Filippini, designed by Francesco Borromini in the second quarter of the 17th century in Rome. The perspective niche in its façade appears to be a literal three-dimensional transcription of a graphic convention adopted in the presentation drawings. To understand the context and the reasons for this “translation”, this article historically frames the theme of the facade intended as a mask and its implicit representational qualities, which can configure it as an autonomous work from the building itself; it frames the interferences between architecture and its image in the era of the advent of pseudo-projective representation and the resistance it finds; it focuses on the facade of the Casa dei Filippini and its perspective niche, here surveyed and photo-modeled to determine the size and relationship between the actual and the perceived shape. Through these methodological and operational premises, the article reconstructs the original center of the façade deformation and analyzes the fictitious value of the facade, as testified by Borromini’s attempt to orient its perception through the drawings of his Opus Architectonicum and those derived from them, eventually confirming the two-way relationship between form and representation.

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Section: From Drawing To Buildingmentioning

confidence: 99%

Borromini, the Casa dei Filippini and the Two-Way Relationship between Representation and Architectural Form

Colonnese,

Carpiceci

2023

Architecture

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“…The section initiates discussions on designer-authored form-generating processes in addition to conversations on the algorithmic undergirding of drawing production. The latter is exhibited in different instances: from the instructions for the reproduction of variations of architectural elements 14 to the mathematical instructions present at the core of our "digital" drawing tools that may reveal some of the "blackboxed" processes of design software.…”

Section: Lecture Course: Digital Representationmentioning

confidence: 99%

Performing Form: Judgement and Subjectivity in Algorithmic Architectural Design

Vardouli¹,

Sabourin²

2019

Practice of Teaching | Teaching of Practice: The Teacher’s Hunch

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It is an oft-made claim that digital computers are changing architectural discourse and professional practice. These changes are plural, varied, and often prosaic. They do not fit one definition of “digital architecture”, nor one manifesto of “digital revolution.” While historians, theorists, and ethnographers of architectural practice are beginning to map the disciplinary valencies and professional effects of digital computers, architectural curricula grapple with questions about when, where, how, and why to introduce computers in an architecture student’s education.1 Professionally accredited architecture curricula negotiate a stifling demand for student proficiency in various kinds of commercial software, with the broader pedagogical possibilities that emerge from the many variances of computational design and making.2 In the parts of a curriculum that integrate a “digital” component, this negotiation usually manifests as a dilemma between training students in software skills and teaching computational processes of thinking, designing, and making architecture. In courses that teach software, computational techniques are often hidden, or “black boxed,” behind the screen. Students deploy them indirectly (through software interfaces) to produce drawings, output construction documents, simulate, and analyze a design’s various performances. Meanwhile, in courses that focus on computational thinking and making, rules and algorithms are out in the open and take on an active role in the creation of architectural space and form.These two approaches echo distinct attitudes toward design processes themselves that surrounded early work on design and computing. In a report on the first international conference of the Design Methods Group—a North American “coalition” of researchers working on “rational” theories and methods of environmental design,3 often through the use of digital computers—architect and urban designer Jonathan Barnett called these two attitudes “black box” and “glass box.”4 “Glass box” approaches were concerned with an analyti-co-mathematical rendition of the design process—asking the question of whether architectural design, or rather which parts of it, could be conceived as a kind of computation: a step-wise process amenable to logico-mathematical description and analysis. Examples of “glass box” work included systematic methods for “fitting” geometric form to functional goals and various methods for enumerating possible geo-metric configurations based on certain rules and constraints, broadly falling under the label of “generative design.” “Black box” approaches, on the other hand, aspired to enhance specific tasks that designers faced in a traditional process through the aid of new graphical and interactive technologies. “Black box” examples included computer aids of different kinds, from drafting tools to conversational interfaces that informed the designer about the impacts of their decisions. In other words, “glass box” approaches recast design as a kind of computation (a step-wise, algorithmic process), while “black box” approaches used computation as a tool for various familiar design tasks.

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“…During the sixteenth century, however, architects also started to calculate with numbers. At this time, modern numeracy spread rapidly across Europe in all domains of life (Carpo 2003). Giacomo Barozzi da Vignola (1507-1573) inserted proportional measurements, written in Hindu-Arabic numbers, in the images of his Regola delli cinque ordini d'architettura (c. 1562-1563).…”

Section: Innovative and Original Aspectsmentioning

confidence: 99%

“…As late as 1641, Carlo Cesare Osio (b. 1612) published Architettura civile, in which he attempted to return architecture to a state of pure geometry, without the use of numbers (Carpo 2003;Fig. 3).…”

Section: Innovative and Original Aspectsmentioning

confidence: 99%

“…7). Appearing in more than 250 editions, Vignola's Regola delli cinque ordini was the most authoritative text on the architectural orders until the beginning of the twentieth century (Evers and Thoenes 2003;Carpo 2003). Printed with copper plates, the illustrations took center stage, with the text reduced to the minimum.…”

Section: The Canonization Of the Architectural Ordersmentioning

confidence: 99%

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Architecture

Raedt¹

2016

Encyclopedia of Renaissance Philosophy

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During the Renaissance in Europe, between roughly 1300 and 1650, a number of intellectual discourses and practices helped shape the discipline of architecture. This article is not about canonical buildings or the evolution of distinctive stylistic characteristics but rather six key topics within an overall threefold structure: heritage and rupture with the tradition, innovative and original aspects, and impact and legacy. The six topics are geometry as the scientific foundation of architecture; humanism, antiquarianism, and the recovery of ancient architecture; architectural histories and the creation of an all'antica architecture; the canonization of the architectural orders; the production of architectural theory; and disegno and the use of architectural drawings. Intellectual history, rather than an art history of styles, is the general approach. It begins with a history of the term "Renaissance" and its application to architecture.

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Drawing with Numbers: Geometry and Numeracy in Early Modern Architectural Design

Cited by 40 publications

References 12 publications

Borromini, the Casa dei Filippini and the Two-Way Relationship between Representation and Architectural Form

Borromini, the Casa dei Filippini and the Two-Way Relationship between Representation and Architectural Form

Performing Form: Judgement and Subjectivity in Algorithmic Architectural Design

Architecture

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