Reconstructing Early Islamic Geometries (original) (raw)
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PRACTICAL GEOMETRIES IN ISLAMIC COUNTRIES : The Example of the Division of Plane Figures
The division of plane figures is a geometrical chapter developed in numerous works written in Arabic. In the extension of Greek practices, this chapter is also found in original developments in Islamic countries. The aim of the presentation is to show the diversity from several books of the Muslim Orient and Occident from the 9th century until the 14th century. This diversity is first based on the multiple origins of the problems. They are linked, among others, to the practices of craftsmen, architects, or jurists. For example, jurists had to decide on the sale or the sharing of fields. To divide a geometrical figure in a certain number of similar figures is an important problem for the decorators who embellished palaces, madrasas, and other mosques and mausoleums. Moreover, these problems are illustrated in some writings of eminent geometers. This diversity also expresses itself by the wealth of procedures of construction and resolution for which the whole mathematical knowledge is included.
The Vocabulary of Perception and Design of Islamic Geometric Patterns
WIT Transactions on The Built Environment, 2018
This paper introduces a methodological distinction between three different scholarly interpretations of the forms and meanings of geometric ornaments in our heritage of Islamic art and architecture: an external cultural position, an esoteric religious argument, and an internal scientific approach. The major part of the paper is then directed beyond cultural allegiances or prescriptions of the Islamic faith and revolves instead around the internal formalistic and purely aesthetic aspects of reconstructing and making of geometric patterns, with the aim of exploring their vocabulary of perception, and their generative principles and inherent processes. The analysis starts at the very basic level where geometric patterns can be perceived as packing of open or enclosed surface polygons or linear configurations. Other means of perception relate to polygons' apparent and inherent geometry, tone or colour, and the application of a quasi-third dimension either through figure-ground reversal or by perceiving linear designs as interlocking elements beyond the 2d plane. The paper then investigates the relationship between means of visual perception and the inherent repetition, geometry and symmetry of patterns on the level of constituent polygons, repetitive tiles, and the design as a whole. Beyond the narrow meanings of likeness and identity in bilateral symmetry, alternative concepts of symmetry are introduced and then applied in setting up a comprehensive vocabulary of 2d geometric patterns based on the classification discovered by crystallographers and developed by mathematicians. The paper concludes by demonstrating the power of combining geometric and symmetry systems in recreating traditional designs or generating new patterns.
Evolution of Islamic Geometrical Patterns
Global Journal Al Thaqafah, 2012
Although Islam gives function and not form, Islam as a context has affects on forms and ornaments in somewhat. The great role of geometry in Islamic architecture due to restriction of using natural figures is an example. In this research, the application of Islamic geometrical patterns (IGPs), and suitability of their usage over architectural elements in terms of timescale accuracy and architectural-style matching is studied. A detailed survey of hundred wellsurviving buildings throughout the Muslim world of architecture has been conducted for this purpose and as a result, not only origin of patterns identified, but also radical artistic movements throughout the history of Islamic geometric ornaments revealed. Finally, this study sketches the evolution of IGPs through history, while regional diversities are also taken into account.
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, 2015
Geometric patterns in two and three dimensions comprise one of the key characteristics of arts and architecture of the Islamic world in many cultural traditions from the central Islamic lands of the Middle East to Spain, India, Indonesia, and sub-Saharan Africa (Bloom & Blair, 2009; Broug, 2013; Ettinghausen, Grabar, & Jenkins-Madina, 2001; Gerdes, 1999; Hillenbrand, 1994, 2009). Although geometry is present, either by conscious human choice in design or as an inherent feature of architectural production in all cultures, it seems to have assumed a much higher significance in Islamic centers of civilization (Grabar, 1992). Often attributed to a proscription against figural images, this interpretation is not borne out historically with reference to palace wall painting, ceramics, ivory, woodwork, and book illustration rich with pictorial narrative. There are, indeed, other more rational explanations for the emphasis on geometric figures (Allen, 1988; Freedberg, 1989; Belting, 2011) as well as many unanswered questions (Grabar, 1992). From the eleventh century throughout the central Islamic lands, the clustered and segmented vaults of muqarnas were used to effect spatial transitions for domes, vaults, and arches, or as a corbel to support balconies and cornices (Bloom, 1988; Tabbaa, 1985), exhibiting elaborations in succeeding centuries (Al-Assad, 1995; Golombek & Wilber, 1988). Simultaneously, one may trace the development of patterns in the plane from the empirical juxtaposition of geometric shapes to more complex arrangements with networks of intersecting polygons, which suggest direct relationships to academic studies of geometry in the Euclidean tradition (cf. Allen, 2004, who argues against such an interpretation). Yet precise intersections between the histories of architecture and mathematics have not been fully elucidated (Berggren, 2008; Bier, 2012; see also, Necipoğlu, 2015).
The use of Geometry in Islamic Architecure-SOHIAB AHMED JAVED (PU)
This paper is basically about how Geometry is used in Islamic Architecture specifically in the region of Sub-Continent. So I would like to take a start from one can say that perfection encompasses both the beauty (Kamal) and majesty (Jalal) represented in Jamal (Perfection). Here, I will mention about the relationship of Scared Geometry and Islamic Architecture with the help of examples that how they merge to show the mightiness of Allah Almighty. Further I will relate the concept of oneness of Allah Almighty with the help of the Masters Work in Sub-Continent. The purpose of this paper is to identify theoretical spirations and practical tools in the making of and representation of Islamic architectural space. it also analyzes geometric principles and design features of traditional Islamic patterns, involving geometric proportion analysis. It also describes the syntheses of Islamic patterns from the perspectives of Islamic cosmology, philosophy, metaphysics, and mathematics.
Beyond Flat Surfaces Parametric Derivations of Historical Islamic Geometric Designs
Architecture and Planning Journal (APJ)
This paper sets out to identify a guiding methodology and define algorithms to extend the existence of Islamic geometric designs beyond flat surfaces. The paper discusses two computational approaches to deriving various non-flat geometric compositions: Euclidean Point Extrusion and Curved Surface Fitting. The paper examines historical precedents, conducts an in-depth analysis of patterns employed to generate those elements, then establishes a computational process to explore the potential of translating 2D Islamic Geometric Designs into 3D non-flat surfaces.
Cultural and Mathematical Meanings of Regular Octagons in Mesopotamia: Examining Islamic Art Designs
Journal of History Culture and Art Research
The most common regular polygon in Islamic art design is the octagon. Historical evidence of the use of an 8-star polygon and an 8-fold rosette dates back to Jemdet Nasr (3100-2900 B.C.) in Mesopotamia. Additionally, in ancient Egypt, octagons can be found in mathematical problem (Ahmose papyrus, Problem number 48), household goods (papyrus storage), architecture (granite columns) and decorations (palace decorations). The regular octagon which is a fundamentally important element of Islamic art design, is widely used as arithmetic objects in metric algebra along with other regular polygons in Mesopotamia. The 8-point star polygon has long been a symbol of the ancient Sumerian goddess Inanna and her East Semitic counterpart Ishtar. During the Neo-Assyrian period, the 8-fold rosette occasionally replaced the star as the symbol of Ishtar. In this paper, we discuss how octagonal design prevailed in the Islamic region since the late ninth century, and has existed in Mesopotamia from Jemdet Nasr to the end of third century B.C. We describe reasons why the geometric pattern of regular polygons, including regular octagons, developed in the Islamic world. Furthermore, we also discuss mathematical meanings of regular polygons.
Evolution of Islamic geometric patterns
Frontiers of Architectural Research, 2013
This research demonstrates the suitability of applying Islamic geometrical patterns (IGPs) to architectural elements in terms of time scale accuracy and style matching. To this end, a detailed survey is conducted on the decorative patterns of 100 surviving buildings in the Muslim architectural world. The patterns are analyzed and chronologically organized to determine the earliest surviving examples of these adorable ornaments. The origins and radical artistic movements throughout the history of IGPs are identified. With consideration for regional impact, this study depicts the evolution of IGPs, from the early stages to the late 18th century.
2016
The topic of this chapter is the geometry and the construction of vaulted and decorative systems called ‘muqarnas’, one of the most typical elements of Islamic architecture. This way of ‘vaulting spaces’ or building roof and decorations with a system of regular staircase-elements that break down the surface covering it with simple geometrical figures, so as to make up complex patterns, spreads throughout Arabic countries, leading to the development of several styles, deriving from different generative geometries, and from building techniques and used materials. The reason which accounts for the widespread development of this type of decoration is to be found in the prohibition of the Moslem religion to portray idols or anthropomorphic figures of God, in contrast with the decorative techniques of sculpture and painting characterizing Christian art. The geometrical study which is at the basis of the Islamic art of decorating is arousing new interest and attention as regards the new sy...