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2012 | Book

Persian Architecture and Mathematics Read chapter Read first chapter

Persian Architecture and Mathematics

Editor: Reza Sarhangi

Publisher: Springer Basel

Book Series : Nexus Network Journal

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

This volulme features eight original papers dedicated to the theme “Persian Architecture and Mathematics,” guest edited by Reza Sarhangi. All papers were approved through a rigorous process of blind peer review and edited by an interdisciplinary scientific editorial committee. Topics range from symmetry in ancient Persian architecture to the elaborate geometric patterns and complex three-dimensional structures of standing monuments of historical periods, from the expression of mathematical ideas to architectonic structures, and from decorative ornament to the representation of modern group theory and quasi-crystalline patterns. The articles discuss unique monuments Persia, including domed structures and two-dimensional patterns, which have received significant scholarly attention in recent years. This book is a unique contribution to studies of Persian architecture in relation to mathematics.

Table of Contents

Frontmatter

Letter from the Editor

Persian Architecture and Mathematics
Abstract
NNJ editor-in-chief Kim Williams introduces the papers in NNJ vol. 14, no. 2 (Autumn 2012).
Kim Williams

Letter from the Guest Editor

Persian Architecture and Mathematics: An Overview
Abstract
NNJ Guest Editor Reza Sarhangi introduces the Editorial Committee for this issue: Carol Bier, B. Lynn Bodner, Douglas Dunham, Mohammad Gharipour, and Hooman Koliji, and the papers dedicated to Persian Architecture and Mathematics in NNJ vol. 14, no. 2 (Autumn 2012).
Reza Sarhangi

Persian Architecture and Mathematics

Touring Persia with a Guide Named … Hermann Weyl
Abstract
A journey across the lands that were part of Persia long ago offers a friendly introduction to symmetry and symmetry groups, as presented in Hermann Weyl’s seminal and popular book, Symmetry (1952). Weyl’s intent was to show how geometrical transformations first, then mathematical structures, could be better understood from a cultural point of view through art and architecture. Our intent is to provide a complementary set of selected pictures of Persian monuments to illustrate Weyl’s ideas. Following the master, we have focused on different kinds of symmetries, starting from the simplest and oldest to those that are more complex, disregarding chronology or geography within the lands of Persia.
Alain Juhel
A Study of Practical Geometry in Sassanid Stucco Ornament in Ancient Persia
Abstract
This paper attempts to survey the use of practical geometry in Sassanid stucco ornament in Ancient Persia to understand the construction of geometrical structures and the progressive process of practical geometry. By use of geometrical analysis, we trace changes of ornament and extract the underlying geometrical structure; we also use symmetry groups, the seven frieze groups and the seventeen wallpaper groups, in order to arrive at a deeper understanding of practical geometry in Sassanid stucco ornament. These analyses will evince features of Sassanid stucco ornament such as: motifs as part of the whole; rotational symmetry and repetition of motifs in linear networks; application of complicated geometrical structures with rotational or reflection symmetry; the planning of whole decorative panels. Also, analyzing the Sassanid stucco panels allows us to discover their repetitive units, which are then classified according to frieze and wallpaper groups.
Mahsa Kharazmi, Reza Afhami, Mahmood Tavoosi
The Decagonal Tomb Tower at Maragha and Its Architectural Context: Lines of Mathematical Thought
Abstract
Of several brick tomb towers constructed at Maragha in western Iran before the Mongol conquests, one in particular, Gonbad-e Qabud (593 H. / 1196–97 C.E.), has generated significant recent attention for its unique patterns with pentagons and decagons. Gonbad-e Qabud is also unusual in having a decagonal plan. While both plan and decoration distinguish it from earlier and later towers at Maragha and elsewhere on the Iranian plateau, the ornamental patterns follow a long line of experimentation with geometric expressions that grace many pre-Mongol buildings in Iran. This article examines in particular the overlapping polygons and radial symmetries of the tympanum of the cubic Gonbad-e Sork (542 H. / 1148 C.E.) at Maragha, and the pentagons and squares of the tympanum of the later octagonal tomb tower (486 H. / 1093 C.E.) nearby at Kharraqan. Drawing from archival sources (plans, elevations, photographs), analysis of plane patterns, and comparative architectural data, this article reevaluates the cultural significance of Gonbad-e Qabud, seeking to situate it within the histories of mathematics, architecture, and the arts.
Carol Bier
Significance of Conical and Polyhedral Domes in Persia and Surrounding Areas: Morphology, Typologies and Geometric Characteristics
Abstract
The aim of this paper is to identify the unique features of the conical and polyhedral domes which topped a majority of distinct tomb towers during the early Islamic era. As opposed to previous general historic studies, this paper introduces a new analytical approach which allows the complete comprehension of the formal architectural language of conical and polyhedral domes based on an epistemological premise of their space syntax. Through an analytic review of selected examples, the paper suggests and addresses the origin of conical domes, their formal morphological compositions and typological forms based on the number of their external shells from the Seljuk era throughout the Timurid period in Iran and nearby regions. The theoretical framework for the formal language of conical and polyhedral domes sheds new light on undiscovered information about the essential characteristics of Persian domes in this region.
Maryam Ashkan, Yahaya Ahmad
Revisiting the Squinch: From Squaring the Circle to Circling the Square
Abstract
“Squaring the circle,” constructing a square that has the same area in a given circle using compass and straightedge, has long been a subject for intellectual investigations among mathematicians and philosophers from antiquity to the pre-modern era. The search for this unattainable ideal articulation found its way into Persian architecture with a different approach: circling the square. This architectonic approach, complementing the philosophical view, started from the square at hand, the chamber, to the circle of the vault. The transformation of the cubic to the domical space is mediated through the squinch, intermediary structural element that unifies the two structures. The two seemingly opposite directions of transforming of one form to another (i.e., square to circle or vice versa) allude to the metaphysical and material attributes involved in this process. This paper discusses the mutual relationship between the intellectual and material transformations and the intermediary role of the squinch.
Hooman Koliji
From Sultaniyeh to Tashkent Scrolls: Euclidean Constructions of Two Nine- and Twelve-Pointed Interlocking Star Polygon Designs
Abstract
In this paper we will explore two nine- and twelvepointed Islamic star polygon patterns consisting of “nearly regular ” nine-pointed, regular twelve-pointed and irregularlyshaped pentagonal star polygons. The two designs are similar in that they may both be classified mathematically as being p6m patterns with the major star polygons placed in identical locations within each layout; however, the structure of the major stars is quite different. Both of the patterns considered here are of Persian origin. The first design may be found as a repeat unit sketch of the Tashkent Scrolls, and exists as a Timurid-style stone inlay and mosaic tiling in India. The second pattern may be found as Plate 120 of Bourgoin’s Arabic Geometrical Pattern and Design and exists as a stucco/plasterwork ceiling in the Mausoleum of Sultan Oljaytu in Sultaniyeh, Iran, as well as numerous other locations across the Islamic world. Both patterns may be recreated via plausible Euclidean “point-joining” constructions (that is, using only the methods available to medieval artisans) in an attempt to ascertain how the original designers of these patterns may have determined the proportion and placement of the stars.
B. Lynn Bodner
Using Christopher Alexander’s Fifteen Properties of Art and Nature to Visually Compare and Contrast the Tessellations of Mirza Akbar
Abstract
When one looks closely at the tessellations designed by Mirza Akbar in the early nineteenth century there are many overlapping structures interacting with one another. The complex structure of these tessellations results from the horizontal, diagonal, and radial grids that were used to construct the tessellations. This paper will discuss how Mirza Akbar constructed two of his tessellations and why star shapes embedded in complex symmetrical patterns are important in Islamic culture, and will then test the usefulness of Christopher Alexander’s fifteen properties of art and nature as an additional method of comparing and contrasting the visual characteristics of these tessellations. The fifteen properties are levels of scale, strong centers, boundaries, alternating repetition, positive space, good shape, local symmetries, deep interlock and ambiguity, contrast, gradients, roughness, echoes, the void, simplicity and inner calm, and not separateness.
Carl Bovill
Interlocking Star Polygons in Persian Architecture: The Special Case of the Decagram in Mosaic Designs
Abstract
This article analyzes a particular series of Persian mosaic designs illustrated in historical scrolls and appearing on the surfaces of historical monuments. The common element in these designs is a special ten-pointed star polygon, called a decagram for convenience; it is the dominant geometric shape in several polyhedral tessellations. This decagram can be created through the rotation of two concentric congruent regular pentagons with a radial distance of 36° from each others’ central angles. To create a decagram-based interlocking pattern, however, a craftsman- mathematician would need to take careful steps to locate a fundamental region. A modular approach to pattern-making seems to be more applicable for this design than compass-straightedge constructions. Such designs include patterns that are sometimes called aperiodic or quasi-periodic tilings in the language of modern mathematics.
Reza Sarhangi

Other Research

Research

A Geometrical Analysis of the Layout of Acaya, Italy
Abstract
The analysis of the urban fabric contained within the city walls of the town of Acaya, made possible by a new integrated survey involving manual, topographical, photogrammetric and 3D laserscan techniques, has cast doubts on the conventional attribution of the city layout to Gian Giacomo dell’Acaya. A rectangular layout consisting of six blocks divided by six longitudinal streets and three lateral streets is indicative of a medieval date. The geometrical analysis shows how the site of the ancient town of Salappya was transformed by Charles I d’Anjou in 1273, renaming it Segine, and how, in about 1500, Alfonso dell’Acaya enlarged the city and its walls according to the same proportional criteria. In 1536 Gian Giacomo dell’Acaya succeeded his father as Baron, redesigning the city walls in order to make them suitable lines of defense against firearms, renaming the city Acaya.
Giampiero Mele
A Geometrical Analysis of the Mausoleum of Sheikh Zāhed-e Gīlāni
Abstract
This article aims to explore some geometrical schemes that can be supposed to underlie the design of the mausoleum of Sheikh Zāhed-e Gīlāni, a monument dating back to fifteen century in northern Iran. The investigation shows that there are intricate geometrical relations among the elements composing the façade of the monument. An isosceles triangle and a regular octagon inscribed in a square, together with some other related lines, form the geometrical master diagram that determines the design of its façade. The findings of this research are compatible with the opinion that geometry played a decisive role in the Timurid/Turkmen style of architectural design.
Mojtaba Pour Ahmadi
Backmatter
Metadata
Title
Persian Architecture and Mathematics
Editor
Reza Sarhangi
Copyright Year
2012
Publisher
Springer Basel
Electronic ISBN
978-3-0348-0507-0
Print ISBN
978-3-0348-0506-3
DOI
https://doi.org/10.1007/978-3-0348-0507-0

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