The Decagonal Tomb Tower at Maragha and Its Architectural Context: Lines of Mathematical Thought

Bier, Carol

doi:10.1007/s00004-012-0108-6

Cited by 16 publications

(4 citation statements)

References 23 publications

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“…Five-fold symmetry consists of a "large regular decagon with an interstitial pentagonal star such that the length of the side of the decagon equals the edge length of the interstitial star". The extant and most well-known examples of patterns generated by aperiodic symmetry are the Gonbade Qabud tower in Maragha during the twelfth century and the Darb-i Imam shrine in Isfahan, Iran during the fourteenth and fifteenth centuries [51,52]. Other studies found some evidence for the presence of quasiperiodic IGPs in western Islamic art, including details [53], octagonal and decagonal types [54][55][56], muqarnas dome [57,58], and the multigrid generation method [59,60].…”

Section: Aesthetic-based Criteriamentioning

confidence: 99%

“…Scholars like Cromwell [66] and Chorbachi [10] believe Islamic artists have had the tools to construct quasiperiodic designs without the theoretical framework to appreciate the possibility or significance of doing so. However, Bier [52] believes that folio 180a, a design from Al-Buzjani [67], may have been used as the generative form of a planar pattern of overlapping decagons related to the aperiodic decagonal/pentagonal pattern on the Gonbad-e Qabud. The aperiodic tiling method was introduced to the modern world much later by Roger Penrose [68], who discovered quasicrystal tiling systems in the 1970s using non-crystallographic symmetry.…”

Section: Aesthetic-based Criteriamentioning

confidence: 99%

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Application-based principles of islamic geometric patterns; state-of-the-art, and future trends in computer science/technologies: a review

Azari

Bemanian²,

Mahdavinejad³

et al. 2023

Herit Sci

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Currently, there is a tendency to use Islamic Geometric Patterns (IGPs) as important identities and cultural elements of building design in the Middle East. Despite high demand, lack of information about the potential of IGPs principles have led to formal inspiration in the design of existing buildings. Many research studies have been carried out on the principles of IGPs. However, comprehensive studies relating to new possibilities, such as structure-based, sustainable-based, and aesthetic-based purposes, developed by computer science and related technologies, are relatively rare. This article reviews the state-of-the-art knowledge of IGPs, provides a survey of the main principles, presents the status quo, and identifies gaps in recent research directions. Finally, future prospects are discussed by focussing on different aspects of the principles in accordance with collected evidence obtained during the review process.

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Section: Aesthetic-based Criteriamentioning

confidence: 99%

Section: Aesthetic-based Criteriamentioning

confidence: 99%

Application-based principles of islamic geometric patterns; state-of-the-art, and future trends in computer science/technologies: a review

Azari

Bemanian²,

Mahdavinejad³

et al. 2023

Herit Sci

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show abstract

“…Pentagonal symmetry and the golden section based 2D patterns in particular are studied in articles by Lu and Steinhardt (2007), Makovicky (1992), Fleurent (1992), Chorbachi and Loeb (1992) and Sarhangi (2012). Multilayered patterns are studied by Bier (2012). The pattern based on a rectangular triangle that has its longest side equal to the sum of its shortest side and its height is studied by Özdural (1995, 2000, 2015).…”

Section: Review Of the Literaturementioning

confidence: 99%

An Alternative Approach to Geometric Harmonization of the Great Mosque in Córdoba

Nanić

2021

Prostor (Online)

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This research constitutes an alternative to proportional composition studies of the original Great Mosque and its four extensions in Córdoba, based on diagonals of a square and rectangles in ratio 1:√2 and 1:√3 (Fernández-Puertas, 2000, 2008). The method for this alternative research consists of graphic analyses by iteration of hypothetical products of the golden section in AutoCAD 2D software conducted on architectural drawings of the original Great Mosque and its four extensions, in reconstruction, according to measurements from the relevant literature. The alternative method insists on geometric harmonization derived from only one starting length in all drawings of same scale. It resulted in the production of a single harmonization pattern based on the golden section, with an additional sequence of a√2/Φn, successively developed for the original monument and its four extensions. It also includes otherwise excluded basic composition elements (minarets) and reveals otherwise hidden proportional qualities. The alternative approach enabled a deduction of algebraic expressions having only one variable for all drawings of the same scale. Their arithmetic values and deviations from real dimensions are calculated. Geometric harmonization by golden section with another starting length is applied to the drawing of the elevation at a different scale.

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“…Recently there has been a renewed interest on that type of Persian Islamic star patterns from different points of view especially for its relationships with cuasi-crystals. (Rull Pérez,1987), (Bonner, 2003), (Lu and Steinhardt, 2007a y b), (Saltzman, 2008), (Cromwell, 2008), (Prange, 2009), (Cromwell and Beltrami, 2011), (Hogendisjk, 2012) and (Bier, C. (2012). Aside from ornamental Islamic star pattern we can regard in historic Persian architecture there are very interesting documents known as Topkapi Scrolls (Necipoglu, 1995) dated to the XVI century (Topkapi Palace, Istanbul, Turkey).…”

Section: Aperiodic Tilings and Other Tilingsmentioning

confidence: 99%

Artisan procedures to generate uniform tilings

Fernández-Cabo¹

2014

imf

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This paper try to prove how artisans could discover all uniform tilings and very interesting others using artisanal combinatorial procedures without having to use mathematical procedures out of their reach. Plane Geometry started up his way through History by means of fundamental drawing tools: ruler and compass. Artisans used same tools to carry out their ornamental patterns but at some point they began to work manually using physical representations of figures or tiles previously drawing by means of ruler and compass. That is an important step for craftsman because this way provides tools that let him come in the world of symmetry operations and empirical knowledge of symmetry groups. Artisans started up to produce little wooden, ceramic or clay tiles and began to experiment with them by means of joining pieces whether edge to edge or vertex to vertex in that way so it can cover the plane without gaps. Economy in making floor or ceramic tiles could be most important reason to develop these procedures. This empiric way to develop tilings led not only to discover all uniform tilings but later discovering of aperiodic tilings.

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The Decagonal Tomb Tower at Maragha and Its Architectural Context: Lines of Mathematical Thought

Cited by 16 publications

References 23 publications

Application-based principles of islamic geometric patterns; state-of-the-art, and future trends in computer science/technologies: a review

Application-based principles of islamic geometric patterns; state-of-the-art, and future trends in computer science/technologies: a review

An Alternative Approach to Geometric Harmonization of the Great Mosque in Córdoba

Artisan procedures to generate uniform tilings

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