Geometry, Craft, and Architecture: Lines of Intersection

The proposed panel focuses on documentation of the relation between geometry and architecture in general, and the geometrical constructions and demonstrations of geometers and craftsmen in particular. Given that “correspondences” between similar approaches, methods or designs, however close, may not be sufficient to establish direct historical relations, the papers in this session present their respective documentation and conclusive forms of evidence to propose various ‘lines of intersection’ among traditions of geometry, craft and architecture.

The first paper, “Mapping the Mathematical Mind: Lines of Thought in Islamic Art and Architecture” describes a cultural milieu of mathematics, poetry, architecture, philosophy, and theology, within which the expression “geometry made manifest,” used by the historian Jūzjānī takes on new meaning, offering insight into intersections of the histories of architecture and mathematics. The second paper, “Parallel Footpaths: Micro-Mapping Practical Geometry in Persian Lands,” follows the paths of a unique work on practical geometry, namely the “Book of Geometrical Constructions” of Abū al-Wafā’ Būzjānī, and the parallel transmission of its Arabic and Persian traditions through unique and revealing sources, and what they can tell us about “lines of intersection” and historical relations during the Islamic ‘Middle Ages.’ The third paper, “Drawing on Light: The Craft of Geometric Pattern Windows,” a collaboration of two scholars, addresses the use, ornamentation, geometry, craft, and perception of girih (Islamic geometric patterns) in orosi, a particular form of window in Safavid and Qajar periods in Iran, through which geometric and vegetal patterns are projected to light interior space. The paper explores aspects of geometric patterns in theory and practice and examines vegetal patterns in relation to Persian gardens.

A fourth paper, titled "Two Astrolabes by Persian Astrolabe Makers from the Safavid Era Preserved in the Malek Museum: A Description and Survey of Their Geometrical and Numerical Inscriptions" has been added to the panel by the Conference organizers.


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During the past one hundred and fifty years of Western scholarship on the architecture of Iran, the interpretation of ornament has undergone profound reassessment. Relying upon both textual and visual sources, recent research on geometric patterns constructed of cut brick on Seljuk and post-Seljuk buildings allows for a reinterpretation of these patterns as visual expressions of contemporary mathematical thinking. A substantive change seems to have taken place in the use of geometric patterns around the year 1000 CE. The new style demonstrates a fascination with points, lines, angles, planes, intersecting planes, and three-dimensional muqarnas. This interest in geometry is evident in brick tomb towers at Ghazna, Kharraqan, and Maragha, and in mosques, minarets and madrasas built in Iran, Afghanistan, and elsewhere, and in the stone monuments of Syria and Anatolia. This paper proposes a cultural milieu of mathematics, poetry, architecture, philosophy, and theology, within which the historian Jūzjānī’s expression, “geometry made manifest,” takes on new meaning, offering insight into intersections of the histories of architecture and mathematics.

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This paper focuses on the Arabic and Persian traditions of practical geometry and their rich and long transmission as an extension of the many lives of a single work, namely the Book of Geometrical Constructions, originally composed in Arabic in the late 4th/10th c. by Abū al-Wafā’ Būzjānī. The centrality of this work to both early science and craft is not only due to the unique content of the text itself, and the rare and clear distinction it makes between the geometrical constructions of the craftsmen and the geometrical demonstrations of geometers; it is especially highlighted in this paper for the range of questions, as well as misrepresentations, that both the text and its understudied traditions continuously generate. The paper follows the parallel footpaths of Būzjānī’s text in Arab and Persian lands, as part of the project ‘Micro-mapping Early Science’, presents new and revealing sources for the documentation of transmissions within Persian lands in particular, and marks their 'telling lines' with reference to specific lines of intersection and historical relations during the Islamic Middle Ages at large.

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Prevalent Islamic geometric patterns, namely girih, found their way into the craft of window-making in the Safavid period from the 17th- century onward. Numerous contemporary reports verify the popularity of sophisticated geometric pattern windows through the Qajar period. Once drafted on scrolls, these patterns were translated into wooden bars and muntins and then ornamented using colored glass, making a multi-layered crafted ornament. This practice became one the most tangible uses of practical geometry in late pre-modern Persia.

This paper examines foundations of the use of geometric pattern in window screens across the central and western Persian plateau, and particularly concentrates on orosi, a specific typology of girih window that embraced the highest levels of ornamentation. The paper critically examines the use of geometric patterns along with then-emergent vegetal patterns in the configuration of orosi window in conceptual and concrete terms. This paper examines the motifs of vegetal patterns in regards to elements of Persian gardens.
The paper also articulates the relationship between theory and practice in regards to girih pattern. comparing the processes of conceiving a girih aperture and the actual construction of the window, this paper will highlight similarities and differences in stages of the making of geometric patterns through various mediums, drawing and making.

This presentation will also discuss the perception of this colored geometric pattern in its original cultural context. The projected lit geometry in the interior space and the simultaneous experience of the abstract and naturalistic geometries of the window and the garden expands the discussion of geometric patterns to the entirety of the edifice and landscape, including light. This multi-layered approach in comprehending practical and perceptual tools in micro and macro scales highlights complexities in the craftsmanship of geometric pattern windows

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Among the six standard planispheric astrolabes in the astronomical instrument collection of the Malek National Museum in Tehran, Iran, four are either bad copies or forgeries; however, the remaining two astrolabes (identified as nos. 2064 and 2067) seem to be original and are dated 1051 AH and 1121 AH. This paper will provide a detailed description of them, which includes a discussion of matters related to establishing their precision. My analysis draws some rather interesting conclusions regarding Safavid science, especially regarding the technical proficiency and precision of Safavid-era scientists, something that is often denied inasmuch as many historians have maintained that the Safavid period represents a time of scientific decline.