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The use of Euclidean geometry in the Sasanian Empire urbanism, Ancient City of Goor, Firuzabad, Fars, Iran (Farnam, 2012)
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Geometry is one of the main features in formation of Persian architecture. Research in Persian architecture geometry is impossible without familiar with geometry. This research tries to demonstrate the relationship between the progress of Persian architecture, geometry and mathematics evolution. In this regard, seeks to address the following questi...
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... In other words, for Iranian-Islamic architecture, geometry, at the same time, is science and art. As mentioned above, the objective of Islamic architecture is placed in the sphere of spirituality and wisdom, so geometry helps architects to build up the bodies that are the manifestation of the sacred [1], [2], [3]. ...
The Jameh Mosque of Varamin is one of the few structures manifesting a transformation from Iranian architecture toward Iranian-Islamic architecture. The study presented here tries to deal with some of the geometric principles implemented by Iranian architects to express the concept of unity. The research decodes the sacred architectural elements and illustrates the ideas used to design the Jameh Mosque of Varamin from different aspects. In the first step, geometric principles such as dynamic rectangles, the golden ratio, and the lute of Pythagoras have been discussed. In the second step, the mentioned geometric principles are adapted to the architectural documents of the building. In addition, the general form of the building and the location of the dome are determined, and the hierarchy beginning from the Mosque's entrance to the dome has been analyzed. The results show that the architects tried to induce unity and monotheism through sacred geometry in a predetermined hierarchy. Also, Findings indicate that the Jameh Mosque of Varamin can be considered the intersection of Iranian architectural ideals adapted and integrated with Islamic principles.
... The use of algebraic and geometric principles of symmetry is an innovative way to describe and understand the cultural heritages of a place due to the fact that symmetry abounds in many forms of arts and design (Al-Hassani, 2007;Ebrahimi & Aliabadi, 2014). Symmetry coexists with geometrical elements, rhythm, tonal and coloring schemes. ...
This paper presented the mathematical analysis of the hand-sewn embroidery in Taal, Batangas on a cultural context and perspective. The Burdang Taal or Taal embroidery is a form of Batangueno art that showcases rich symmetrical figures and transformations. The study used the descriptive research design. The analyses made on the figures and designs of Burdang Taal were based on the concepts of group theory and transformational geometry. One hundred twenty-four (124) samples were collected and analyzed using the seven frieze patterns and seventeen symmetry groups or plane ornaments following the International Union of Crytallography (IUCr) notation and classification. Results showed that almost all of the frieze patterns and the plane ornaments are exhibited in the different designs embroidered on the Barong Tagalog and other decors or accessories. Six out of the seven frieze patterns, with the exception of symmetry group mg, were identified. In terms of plane ornaments, nine of the seventeen symmetry groups were identified including cm, pm, pg, p1, pmm, pmg, p4, p3, p6. The dominant plane ornaments were formed mainly using translations, perpendicular reflections without glides, or rectangular lattice without rotations or glides. The study underscored the creativity of the magbuburda or local embroiderers, who were able to express meaningful geometric designs without the necessary mathematical training on crystallography and pattern-making. Important implication of the study would be its contribution to the enrichment of the study of abstract algebra and the geometry of transformation.
... Our knowledge of the history of mathematics in ancient Persia in the pre-Islamic period is at best quite limited, though there are some research papers on practical geometry in Persia and the Persian architecture, written quite recently [22,40]. On the other hand, there are many books and papers on the history of mathematics in Persia in the Islamic period (for example, see [20,30,42,70,77]). ...
This is a short note devoted to the contribution of Professor Gholam Hossein Mossaheb to mathematics and the Persian language.
... This 1453-dating of the Safavid tessellations has been persistent: see, e.g., Lu and Steinhardt (2007), Zheludev and Ozbay (2007) Ebrahimi and Aliabadi (2015), Williams and Ostwald (2015), Aube (2016), Bier (2011Bier ( , 2012Bier ( , 2017 The term Taʿmīr finds its roots in the verb ʿamara which means to build, construct, rebuild, restore, … (Wehr and Cowan 1976: 643). The inscription is compatible with "the addition of new parts" to the existing structure. ...
A particular mosaic at the Darb-e Imam mausoleum in Isfahan has caused some controversy 10 years ago when it was claimed to exhibit quasi-periodic properties and that it was 500 years old. The technical part of this claim has been disputed (and refuted) by several authors. The date, 1453, also a key part of the press coverage that medieval Islamic artisans did advanced mathematics 500 years before the West, has not been challenged. We argue that the panel in question dates from the end of the Safavid period (1715–1717). Techniques developed during the Safavid period seem to be wrongly attributed to the fifteenth century.
... So it can be concluded that geometry was an influential way to design from micro scales e.g. decorations to macro scales, urban designing and royal complexes [8]. ...
... Moreover, by urban development during Sassanid and Parthian era, the tradition of making circular cities continued in some city such as Darabgerd (Figure 9) [9], Goor ( Figure 10) and Khoreh Ardeshir. This fact indicates the usage of geometry in large scales in that time [8]. ...
... During this era, dome has been established on square base with specific techniques which convert square to octagon (√2 ratios), Hexagon, and continue this way until arriving highly close to circle. Moreover, central porch of Kasra palace follows √3 ratios (has a saloon with a length of 60.34m and width of 30.25m) [8]. Since arrival of islam until the ghaznavid dynasty: In early Islam's era, with the gradual development in mathematics, the art of architecture developed too. ...
Iranian Architecture, depending on materials and various factors have various forms, the geometric proportions is one of the factors affecting the form of building in both Structure and decoration. Geometrical shapes in nature have always inspired Iranian architect. As Architecture is closely tied with geometry, orders and proportions over thousands of years, analyzing shapes and finding geometric ratios used in historical monuments and sites can be used in damaged constructions, which need to rebuild or repair. Therefore, this research tries to discover geometry rules in nature and then reveals that architecture is closely related to geometry, too. This Effort has been made by library studies on the one hand and on the other hand is based on field data to achieve geometrical qualities in different periods of Iran. Analyses done by the author revealed that discovery the geometry rules in historical buildings is the first step to rebuild the loosing parts.
... Design appeals are defined by Punter and Bell (2000, 12) as: They also considered the 'bad neighbour' issues, such as day or sun lighting and overlooking property, or privacy, as additional design issues in their analysis. Based on their study, 12 percent of planning application are refused in the UK annually, but only 3 percent of them end up in court; only 0.75 percent of a total number of planning permissions granted in any one year (Ebrahimi & Aliabadi, 2015). Punter and Bell (2000) used two sources of available data to study appeals in England. ...
The visual relationships between a proposed development and the existing urban setting have become increasingly controversial in the past two decades. Protecting and enhancing visual attributes of the current urban environment is regulated by a range of performance-based policies and regulations. However, every year many development conflicts occur between developers, local councils and residents resulting in costly delays in the development process. Visual amenity and character are two of the most contentious issues in these conflicts.
Currently, conflict resolution based on these policies relies on experts’ interpretation of what appears to be visually significant. Although visual amenity experts aim to provide an impartial and objective assessment of visual effects of proposed developments, their evaluations are sometimes mixed with personal judgments and lack enough centrality and reliability. The problem is compounded by the fact that there are no consistent approaches within and between localities and experts as to what is considered visually significant. The uncertainties and inefficiencies created by performance-based planning policies, to regulate the protection of urban visual quality, highlights the importance of developing reliable, measurable and repeatable approaches to analyse visual environments and to describe the urban character.
Based on a postpositivist approach, a range of research methods using exploratory and descriptive approaches was used to answer the stated research questions. Therefore, the research design is split into three stages. The first stage involved reviewing the planning court cases in Brisbane from 2000 to 2012 to identify the overall different types of conflicts within the city. These conflicts were analysed spatially to determine their distribution and to look for any significant spatial patterns. Based on this review, four case studies were selected, and three measurable methods were developed to provide a higher level of quantitative assessment of visual properties of the urban character. In the last stage, the technical methods were evaluated by a panel of three visual amenity expert witnesses to investigate the effectiveness, usefulness and potential of these methods to be applied in expert assessments and court case resolutions.
This research focuses on urban visual amenity conflicts in the city of Brisbane, Queensland, Australia and identifies the gaps and recurring issues inherent in expert assessments and judgments. Based on this knowledge, quantitative methods to assess visual amenity and character, with greater objectivity and reliability than existing methods, have been developed. The outcome of this research contributes to the field of visual assessment and character studies in landscape planning and assists decision makers and Environmental and Planning Courts to determine development conflicts with more objectivity and reliability.
... The occurrence of geometric design language in traditional Persian and modern Iranian buildings reveals the very close relationship between geometry, mathematics, and Persian architecture. The concurrent evolution of these three disciplines is a demonstration of the direct impact of the progress in mathematics and geometry on the development and formation of architectural elements, ornaments, and decorations (Ebrahimi and Aliabadi 2015;Ebrahimi et al. 2014). In particular, in many Persian traditional buildings, geometry is used as a generator of architecture, in both structural elements and decorative forms and patterns (Maleki and Woodbury 2008), such as mosaics and their tiles, rasmi domes, muqarnas, yazdi-bandi, columns, etc. ...
Persian architecture is characterised by shapes and patterns, which can be analysed through mathematical models. Beside 2D patterns, many of the traditional geometric ornaments are realised on 3D surfaces such as domes or vaults. Literature mainly addresses the 3D problem by means of a 2D scheme, which is an important and synthetic representation but is not exhaustive and lacks of clarity. This paper proposes a framework based on the integration of 2D drawings, as in the traditional approach, and a photogrammetric 3D model based on a sample of standard resolution images (tourist pictures). The framework is tested on a muqarnas, a characteristic Persian ornament, in order to study and analyse its modular design and hierarchy of elements. As a case study, the entrance iwan of the Shah Mosque in Isfahan, Iran, is considered. The result is a link between the 3D patterns and the geometry of architectural elements, which completes and overcomes their schematic 2D representation.
Nature is an inspiring source of art and architecture. Sacred
architecture - like Islamic architecture - extracted complex
mathematical relations and geometrical shapes from the structure of
plants and animals to compile a specific architectural style. Added to
the golden ratio and the square ratio, Mameluke architects used
fractal geometry in the design of madrasas. The unique characteristics
of the fractal forms fulfilled the aim of expressing the infinity and the
unity of the universe. In the last four decades, after the fractal theory
by Mandelbrot, architects and mathematicians excreted lots of efforts
to measure the visual complexity in several architectural styles; historic
and modern styles, using fractal analysis. This thesis focuses on
analyzing the complexity of the Mameluke Madrasa plans in terms of
its fractal geometry and the evolution process of its patterned grid. The
fractal grid originated from a central square and then branched to scaled self-similar squares. Since the fractal grid was a major design
generator, therefore the development and outcome of this research
assist architecture theory and history researchers in the comprehension
and analysis of the fractal characteristics of the Mameluke style. Hence,
a style is not reproduced only by the imitation of external architectural
features but could be reused by following the morphogenesis
process of its geometry. In order to achieve the thesis objective, Four
Mameluke Madrasa is selected as an archetype that undergoes the fractal
analysis process due to its simple understandable form. A
computational model is set up to merge the analysis and generation
process together in one interactive parametric model. The average
fractal dimension of the Mameluke Madrasas will be calculated and
inserted in the parametric model to generate design variations. Thus,
the interactive parametric model provides two complementary
functions. It can also be transformed into comparable styles by
changing the scripting code of the parameters and constraints.
Therefore, the presented model is used to generate an infinite number
of variations based on the fractal dimension of a style.
This paper presents a comparative case study on the digital modeling workflows of a particular muqarnas system. After the literature review and the definition of the context, several digital modeling workflows were described as element-based, tessellation-based and block-based workflows by using computer-aided design and parametric modeling software. As the case study of this research, these workflows were tested on a muqarnas design located at the Sultanhanı Caravanserai in Central Anatolia. Then, workflows were compared according to three qualities: analytical, generative, and performative. The outcomes of element-based workflow has more analytical solutions for the study, where tessellation-based workflow has more generative potential and block-based workflow is more performative.
