Symmetries of Islamic Geometrical Patterns

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Kuznetsov, It means that everything was designed, not only in architecture but also in every field of Islamic art, has the specific role and every detail is important to the connection between the world we live and the world after death. As well, all of those patterns have sacral meaning. However, Islamic artists were not just determining the meaning of the patterns; they also made calculations for the perfect proportional structure of patterns. This was very important in the idealistic Islamic world.

The idea expressed by Al-Ghazali, meant that everything was designed, not only in architecture but also in every field of Islamic art, has the particular role and every detail is important to the connection between the world we live and the world after death. As well as all of those patterns have sacral meaning. But Islamic artists were not just determining the meaning of the patterns, and they also made calculations for the perfect proportional structure of patterns.

These comparative studies were considered imperative in the idealistic Islamic world. For a Muslim artists or craftsmen, which were decorating a surface, undoubtedly geometric forms seemed the most spiritually convincing. Because it was directly representing the idea of oneness of the God. We could call this oneness inexpressible, because its nature prevents anything but itself, it is unique. It is reflected in the world due to harmony.

Interlacement expresses the one aspect and the other. But it is yet another respect that is recalls the unity underlying things, namely that it is generally constituted from a single element, a single rope or a single line, which comes endlessly back upon itself. He begetteth not nor is He begotten. In general Islamic geometric patterns are built on circles or squares base.

They are that simple we could draw them with using just a ruler and a compass. Typically, repeated, overlapped and interlaced geometric shapes create complex patterns that consist of a number of polygons repeated many times. The decorative elements deployed use a range of symmetries that have now been classified as belonging to distinct mathematical groups, but the subtlety and beauty of the designs are unparalleled in modern mathematical thinking.

The base of the most geometric patterns could be four-, five- and six folded. All of the others could be constructed from those three types of folding. The natural division of the circle into regular divisions is the ritual starting point for many traditional Islamic patterns.

Harmony is the one of the first important criteria in creating geometric patterns. There are not any special field of science studying harmony. It appears in every detail of pure nature elements. Architects always tried to move this harmony from nature to their works. We could understand all their works as a representation of natural. Symmetry Symmetry is the one of the most important expressions of harmony. When we take a look to the philosophy or nature sciences, we notice that a symmetry could connect and balance the purposes of different schemes patterns for the human art. Even in ancient Greek mythology dragons created a chaos, Gods created symmetry and harmony.

Geometric patterns were used to represent the God, earth, human being, death and life in many cultures. For example, a Japanese Buddhist Sengai Giben who is famous by his writings and teaching used calligraphy and painting to make those teaching more accessible to people. One of the most famous of his paintings is an image of circle, a square and a triangle which represents: sky, man and earth. In the art of the Ancient Greece and Medieval Europe, we see numerous examples of these figures, which are representing the universe. It reflects no ideas but transforms the surroundings by having them share an equilibrium whose center of gravity is unseen Continuity of interlacement invites the eye to follow it, and vision is transformed into rhythmic experience accompanied by the intellectual satisfaction given by the geometric regularity of the whole Study of Islamic art, or any other sacred art, can lead to a profound understanding of the spiritual realities that lie at the root of a whole cosmic and human world.

Burckhardt The problem of drawing of ruled polygons is very important in Islamic geometric art. Mathematics of Islamic period inspired by Romans, used and then improved their techniques of constructing polygons. They did not think that old techniques work and had developed new ones. Polygons with seven and nine edges were the most difficult ones and the problem of drawing them was actual for that time.

However, the mathematics of the Islamic culture understood that it is not possible with the method written below and had written new works just for the construction of seven and nine edged polygons. It is interesting that the famous scientist Abu Rayhan al-Biruni also noted the importance of seven and nine related geometry, when he was observing flowers. He observed that petals of flowers while opening create a circle which in generally complies with the rules of geometry. It is difficult to find a flower with 7 or 9 petals, because through of geometric rules it is impossible to fit them into the circle by dividing in triangles.

It is common to see a flower with three, four, five, six or eighteen but never seven or nine. Drawings by Husein Shen The base of the most geometric patterns could be four-, five- and six folded. Nature and Geometric patterns Natural assets always repeat itself on all progress steps. Thus, to learn harmonic methods of creation we should understand phases of nature creation.

Even every hidden detail of nature sends us a message 3. As we know everything in art and architecture take its start from nature. Symmetric flowers make it much more visible. It can also be seen as the circular flow of time, each point of symmetry marking an interval of time, like the hourly numbers and second marks on a clock face. When the ancients measured time and angles in minutes and seconds they were acknowledging the complementarity of time and space.

The most inexplicable conclusions derived from our analyses were the positioning of the points, usually on the embracing circle, from which the curvature of the petals could be struck as radii. A fine example of this migration of the centers from what would be considered natural comes from the careful analysis of the curvature of the six-pointed or six-petalled flower.

It is a fine example of profundity in simplicity. Sixness is the intrinsic nature of the movement life of a pair of compasses. It calls the Flower of Life, despite the fact that this pattern is rooted to historical period before Christ; the topologically this name is a new term in arts. It was an ancient Phinikkian symbol, which takes its origins of course from nature. Figure 9 Phinikkian ornament "Flower of life" One of the first appearance examples of those patterns is observed in the Idalium, an ancient city in Cyprus. The Temple of Osiris at Abydos have this symbol drawn in red ochre.

Photo taken by Ray Flowers In Islamic geometry it is used as a grid to construct girih Islamic geometric pattern. These connected circles are used in different combinations and create a big variety of different patterns. The first is geometry, which interprets the unity to the space language, the second is rhythm, which is opening the unity of the time and the third is light. The allegory of His light is that of a pillar on which is a lamp. The lamp is within a glass. The glass is like a brilliant planet, fueled by a blessed tree, an olive tree, neither eastern nor western.

Its oil would almost illuminate, even if no fire has touched it. Light upon Light. Allah guides to His light whomever He wills. Allah thus cites the parables for the people. Allah is cognizant of everything.. There is not more perfect symbol of divine oneness than light.

Muslim artist wants to transfigure even the material he is working with to the light vibration. That is point to decorate interior and sometimes exterior surfaces of mosque or palace with ceramic mosaics. Often this decoration limits on lower parts of the walls, like that, the craftsman softens their hardness. It is also the reason of the transformation of their surfaces to perforating transmissive reliefs.

The colors show the internal richness of the light; through the coloristic harmony, we notice the true nature of the light. Especially the Court of the Lions shows how the stone is turned into light vibrations. Figure 12 Sebka decoration and arches. The Court of the Lions. Alhambra palace. They are rhomboid patterns that cover walls, columns, arches etc.

Numbers and patterns As the Islamic geometric patterns are created by using strictly rules. When we analyze them mathematically, we review many mathematical regularities. Numbers played an important role not only on Islamic geometric patterns but also on the whole Islamic philosophy. For example, the importance of the number eight is describing by Keith Crithchlow like that: Eightness is inevitably associated with the diatonic octave and anciently with the planets visible to the naked eye.

Eightness is sometimes called the auspicious number: it is a form of perfection of the earthly order, giving the four cardinal directions and their intermediates. The ear easily registers the eighth note in the diatonic scale as the octave. Eightness is part of the Fibonacci sequence as we saw, so it is likely to arise in the flower world —, which it does in particular in the beautiful flower known as Cosmos as well as in the Clematis and Lotus to which we will be returning.

Figure 14 The squares and the spiral in the Fibonaccci sequence progression. Eightness is associated with paradise. In ancient Persia, gardens were designed and divided into an eightfold pattern. This pattern also spread to India. Not only is there a reference to eight paradises but Islamic mythology offers the model of there being eight angels holding up the throne of God. From a Hadith of the Prophet Mohammed. A Hadith is a traditional saying recorded as being spoken by the Prophet. Spiritual expressions of this number occur widely, the best known probably being the noble eightfold path of Buddhism.

Maybe there is a connection between the vertical 8 and the horizontal sign of infinity? Wasma Chorbachi, a scientist in the field of Islamic art, have written a lot of articles, folios and manuscripts on the topic of spiritual meaning of the geometric patterns and the mathematical approach. The design as given by Critchlow. Bhaskara's proof as given by. Figure 16 shows one of the panels that Chorbachi has studied. The square is divided into four congruent sectors by two perpendicular lines and each sector is divided, in turn, into polygons of three kinds including a symmetric kite shape as shown in Figure 18 a.

Symmetries Of Islamic Geometrical Patterns - Abas Syed Jan, Salman Amer Shaker - Google книги

The key to understanding this tiling is an asymmetric quadrilateral ABDG with proportions V7 inscribed in a circle as shown in Figure 18 6. The sector of the square is obtained by adding two gnomons of unit widths to two sides of the quadrilateral as shown in Figure 18 a.

Figure 18 c shows that similar kites at three different scales can also be found within the tiling. In her article, Chorbachi has generated many of her own tilings based on this asymmetric quadrilateral and its geometric properties. Subdivide a square into four congruent sectors as in Figure 18 a.

It makes a good puzzle, for persons not aware of the origin of the sectors, to put the pieces together to re-form the square. It makes an even better puzzle to put the pieces together to form two squares such as in Figure 18 a. It is interesting that the same panel that Chorbachi sees in strictly geometric terms, Critchlow prefers to think of in spiritual terms.

For example, the solid dodecagon and dotted square in Figure 17 a is Critchlow's doing. His interpretation is The coincidence of twelve and four suggests the zodiacal symbolism controlling or embracing the fourfold axial kite shapes which can be taken to symbolize the four seasons, the four elements, and the four qualities of hot and cold, moist and dry.

Heaven and Earth The arts of the sacred have traditionally always been governed by the sacredness of the tools employed, particularly at the design stage. Critchlow One of the interesting theories was proposed by Keith Critchlow. The teaching of all three major monotheistic religions confirms that the Creation was accomplished in six days. The subject is too extensive and it is inappropriate here to attempt tp enlarge on the meaning of this doctrine. However, it is appropriate to state it is an error of our own times to treat such matters as revelation on an exclusively literal plane.

Inside the twelve we see a set of seven points - the hexagon and its center. These are associated with the seven heavens as one of their symbolic forms. Critchlow The author describes meaning of the symbolism for Islamic architecture and art and particularly in geometry. All of the symbolic elements in Islamic arts and every detail is connected with the sacred book of Muslims Quran.

Even a small surah could be a result of big structures in Islam. It applies to main philosophy of Islam. Another important book with useful reflections have written a scientist Seyyed Hossein Nasr. Geometric rules to create Islamic geometric patterns When we geometrically analyze Islamic geometric patterns, we see that it is possible to create them with the help of the ruler, compass and pencil. Of course, it is possible to analyze them mathematically with the use of different formulas and difficult calculations. To visualize how traditional craftsman worked to create patterns helps to recognize also the way how they was thinking.

Architects in the ancient word used a piece of rope and a piece of wood. The rope was tired to the fixed point in the center of a circle they wanted to draw and the wood was tired to another end of the rope. Master could make a perfect circle by walking round the fixed point. Obviously, the size of the pattern were determined by the size of the rope. The straight lines were been drawn also with the help of the rope by just holding both ends on two points. This method was good for big patterns but for the small ones they need to generate more accurate method. The accuracy is the most important thing to draw a geometric pattern.

The rope method was been replaced by the compass method. For the centuries, Islamic builders were used nonadjustable compass. Because it was very important the circles to be in equal sizes. Construction of geometric patterns in İslamic art mostly consist of repetition of a single motif. So for the covering a big space the craftsman often used a square, hexagonal grid and created a pattern by connecting them with each other. Individual motif is repeated in each geometric unit of the grid.

Sometimes they were connecting different units to cover a space, which does not have strait shape. Every geometric pattern starts with the creating of grid. We always start designing of patterns with a circle. Then we add secondary circles and connect them with straight lines. By this, we determine the basic shape of the patterns.

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Quantity sizes of circles and the way of their intersections' connection should be chosen depended on typology of the pattern. Typology means to which family of patterns our pattern belongs to. There are three common families of patterns. They are four-, five- and six-folded geometry. Most of the others could be created by multiplying number of circles. After the identifying, we draw a geometry inside the circle.

Pentagons are the most difficult geometric shapes to create. They also have some complications on covering a surface. Squares and hexagons are much more easy to fill the surface. Sometimes in geometric patterns, we need combinations of the patterns. As harmony and balance are important criteria in Islamic art. Sometimes it is difficult to represent those feelings just with the geometric lines. Islamic craftsmen used extra detail to make it work more. It could be a vegetal motive or a calligraphic writing. As important elements of Islamic geometric art, Eric Broug shows in the book harmony and balance.

A pattern that is made up entirely of straight lines is incomplete. It needs to add extra decorative elements to be completed, It is possible to bring out the symmetry and richness of a line pattern by adding vegetal motifs, such as flowers and leaves, for example, or color. Bourg, Some of the patterns create interlaced bigger pattern while connecting with each other. Dewdney recently described a practical method of creating homemade Islamic tilings A set of intersecting and self-intersecting lines weave through the tilings, as shown in These lines are unrestricted except for the fact that each must originate and end at the boundary.

If each crossing is alternately designated as either an overpass or an underpass, whenever one arrives at Tilings with Polygons. See Figure Bourgoin with underlying triangular grid. An Islamic pattern by J. A previously designated crossing, it has the required structure. Say one travels along the road bordered on the right by a region of some color. After the crossing, the color on the right changes. Thus one can say that an overpass always leads to, say, the color red on the right while an underpass leads to, say, blue. It follows that the road crossings must be assigned correctly after a cycle.

The first two techniques of decoration involved the medium of construction itself. In Anatolia, where the traditional medium of construction was stone, carved stone became the major medium for ornamentation. The technique is a very ancient one and does not require further elaboration, except on one specific point : in many instances the stone ornaments seem like have been applied to the surface of the wall rather than understood as a part of the fabric of the wall; it always seem artificial as an imitation of something else.

Much more original and different technique than the medieval Islamic use of stone is brick. It used for decorative and as well for the constructive purposes. It is also a good example of the decoration in two levels being connected like a puzzle. In later centuries, it was no longer the only technique of decoration, it was still a major one but the number of uses increased. The manner of creating a brick decoration had changed from linear zigzag patterns into curved dome decoration.

It gives a texture to wall in some examples there were used bricks of different size to get a complicate pattern. In some examples, the effect of brick was artificially created in stucco. The third remarkable technique of Islamic architectural decoration is stucco. Already in pre-Islamic times, whether in western Iran and Iraq stucco had been used to cover walls of palaces and temples, because the medium of construction — rubble in mortar or unbaked brick — was not very impressive and because of richness of surface decoration could create more important effect than barren walls.

There are existed examples with stucco applied to the whole wall without major decoration. It consists of terra-cotta, basically, of ceramic fragments that were specially molded or formed to full some areas or to create a specific geometric pattern. This decoration type was more expressive than stucco and created a big contrast between decoration variations. It was already known in Parthian times in Central Asia. Photo from the website wikimedia. In general, we could divide it in for parts: Baku capital of Azerbaijan region, Nakhchivan region, Sheki region and Karabakh regions. We could notice totally different techniques of pattern creating in all of those regions.

In Baku it is stone decoration, in Sheki and Karabakh it is window and other interior decorations and in Nakhchivan we see it in tombs decorations — stone and glazing methods. We will explore details of decoration in all of those regions in the paragraphs below. Then the idea of making a decorated window out of colored pieces of glass painted with religious motifs and combined in way to form a picture popped up.

Traditionally in stained glass windows of Catholic cathedrals in Europe strips of lead were used as binders. The technique of stained glass production in Azerbaijan and Iran is different from European. Instead of lead, strips of wood are used. A strip of wood has channels where glass is inserted. Channels are normally used in traditional woodwork to connect up two pieces of wood together without using nails. The glass is placed inside channels and wooden strips are glued together. The width of a channel is equal to the glass thickness. In the past a 3mm-thick glass was used, but now, it is mostly of 5 mm thickness.

A panel of wooden stained glass is solid and durable; it can stand a stroke of a man or a strong wind. The design of wooden stained glass based on geometry of a square or a triangle is widespread. Colors are very bright greens, reds, blues and yellows. Sometimes colorless glass is used. In Azerbaijan, ancient town of Sheki is a center for shebeke production and restoration.

Sheki Khan Palace built in 18th century is lavishly decorated with shebeke.

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Just in the Sheki Khan Palace have founded sixteen types of pattern. Along with geometric shapes, there are biomorphic rhomb-shaped motifs. Creating of "shebeke" was performed with connecting strips of wood and pieces of glass. All wood details have special recesses to connect it with glass. That wood pieces also are connecting to each other in that way without using of any glue, nails or any other connector. In Iran wooden lattice windows was used as an architectural feature in all kinds of buildings. Magnificent Nasir al-Mulk Mosque in Shiraz built in the 19th century is famous all over the world for its stained glass decoration.

Ali-Qapu palace and coffee house in Shesh Behesht garden, Madar-e-Shah medresse, old mosques in Isfahan — all of them have wooden grills on their windows. In Iran I noticed that the glass is placed behind the lattice. Marina Allin guesses that it is a result of lattice restoration and historically glass was placed inside wooden cells.

Allin, The spiritual meaning of a stained glass lattice window most likely comes from a contrast between light and the absence of light. Light reveals shape and color; light makes things possible and represent Divine enlightenment. Practically the widespread use of wooden grills as all other kinds of grills in Islamic countries can be explained by the need for protection from a daytime heat. It is one of the features that traditional Islamic architecture has in order to help people to feel comfortable inside the building despite on the temperature outside.

Ashraf Rasulov explained how he creates that magic patterns. He says that in a small detail of a door decorated with shebeke in the one square meter we could be found 14 details. Even a one millimeter mistake could destroy the whole pattern. Every detail should be made by hand: all of the wooden pieces and colorful glasses. Sheki, Azerbaijan. Photo by Alina M.

They were made in stone window decorations. The Sheki Khan's palace was built in during the Kajar dynasty rule period. It was built by Hussein khan, he was also known as a poet under is pen-name Mushdag. It was a summer residence of khan. But this is the only one conserved till nowadays. The palace is a two-story brick masonry structure elongated on the north-south axis. It was covered with a wooden hipped roof with long eaves.

Figure 24 Sheki Khan's Palce. XIIX century. Sheki, Azerbaijan Photo by Niall Henderson In the palace we see arabesques, miniature paintngs, mugarnas and geometric patterns. This makes interior decorations of the palace more active and dynamic. Among the patterns in the palace's "shebeke", we can notice six 6 folded, eight 8 folded and twelve 12 folded geometry.

Photo by Alin M. Reference to the website unesco. However, as we might expect, geometric patterns appear much later. Figure 26 Gobustan rock engravings. Baku, Azerbaijan. The historical part of Baku is full of the Islamic elements in architecture: minarets, window, door elements and etc. He complex of Shirvanshahs palace. Baku, Azerbaijan Photo by Aydan Aghabayli One of the important architectural monuments inside the Old City in Baku is the Palace of the Shirvanshahs, built in the 15th century in the time of Shirvanshahs reign, from the moment where the capital was transferred to Baku in result of the huge earthquake that victimized Shamaha.

The location of this palace on the Baku hill is one of clear dominance and we can see it from afar. Among the medieval structures of Baku, this complex stands out for its architecture, massiveness and decorative features. It is a large and ordained gathering of several buildings consisting on the main building, divankhana, the mausoleum, the palace mosque and the palace bathhouse. We can observe there a big amount of Islamic geometric patterns examples. The main building was built in by the efforts of Shirvanshah Sheykh Ibrahim I. Through the inscription desk with the construction, dates were found only on the mausoleum — and on the minaret of the mosque, — , archeologists and historians could just guess that the mausoleum, the mosque and the palace were built in near dates.

But it could be that the palace was built before, in the first decades of the XV century. For the building itself, it was constructed by phases, the first phase consisting of the central part, followed by the surrounded western part. Divankhana is an eight-edged rotunda — a pavilion with a small courtyard inside made exclusively in stone. The western entrance portal of the rotunda is decorated with arabesques, Arabic inscriptions and geometric patterns. They are inscribed in octagons that are also connected with each other. Ornaments also cover tympanum and windowpanes under the openings.

The portal leads into a passage connecting the hall with a podium placed in the crypt and the service facilities located one above the other. On the southern courtyard near the palace, there is a building of the Mausoleum, where the court scholar Halilullah I Seid Yahya Bakuvi was buried. The internal decoration of the mausoleum consists of an underground crypt where the headstone of Bakuvi and camera is located.

The small octagonal mausoleum volume turns into a drum covered with an outlined dome. On the both sides of the mausoleum, there are three small windows carved in solid slabs of limestone, representing a crosscutting stone lattice consisting of multipath stars. Figure 28Shirvanshahs palace decorative stone "shebeke" window elements. Muqarnas of portals are also carved. Baku, Azerbaijan Photo by Aydan Ahabayli Hexagonal medallions over the arches of Mausoleum of Farrukh Yassar octagonal building on the site of the palace complex, also called Divankhane show stone carved calligraphy.

Inscriptions are written in very ancient Kufic Arabic script. On the left, the inscriptions carved inside the medallion are framed by six geometrical patterns in a rhomboid shape. The hexagonal medallion on the right contains twelve small rhombs. Stone decoration of Baku architecture is superb. It is where the great level of craftsmanship and elegance of artistic expression is shown, the ancient craft of stone carving serving Islamic art. Icheri Sheher. Baku, Azerbaijan..

Other stone carved pieces are gravestones and gravestone panels with a variety of motifs. They are conserved in Icherisheher of Baku. Baku, Azerbaijan Photo by Aydan Aghabayli Figure 32 Examples of the Islamic Geometric pattern on stone decoration of the top of the minaret of the mosque. Baku, Azerbaijan Photo by Aydan Aghabayli Those traditional types of Islamic geometric patterns decorations are used until nowadays in the modern architecture in Baku. Figure 33 Modern interpretation of Islamic Geometric patterns. And invorlving them to the new building in stone "shebeke" window detail. And invorlving them to the new building in window decoration detail.

Islamic geometric patterns in Nakhchivan Wide variety typifies examples of patterns in monuments of Nakhchivan. When we study the origins of architectural decorations and ornaments, we could see that arts are an integral part of the society. The Ottoman Empire period left an important mark on the arts and the architecture in Nakhchivan region. Turkish art originates entirely on nature elements.

Every detail and every line of that art is life and action. Decorative elements in the designs are quite expressive in that matter. All of the figures have some vitality, as they appeared with the influence of a totemic thought. Thus, forms taken from nature were been transformed to patterns and its vitally lines braked, delayed and become flat. We must stress, however, that Nakhchivan architecture style is different from the others that existed in Azerbaijan.

It uses brick as construction material and applies colored glazed tiles especially turquoise for geometric pattern decoration. The most important examples are within the class of mausoleum architecture. We could recognize the architectural style of the period where a large amount of Islamic geometric patterns still stand today as a proof on the huge variety of decorative solutions.

Patterns are glazed, carved in stone or brick, created with bricks laid as a pattern. As well as ways of application the patterns itself are also various. In mathematical approach, we could differ their models with 4-, 6-, 8-, and folded geometry, fig. Their construction period of them is dated to the XII century, which is date of rule of the Seljuks empire.

The most important buildings of the 12th century were designed and directed constructed by famous Azerbaijani architect Ajami ibn Abubakr Nakhchivani. It attracts attention with its simple geometric form and nice harmonic structure. The mausoleum itself has an eight-pointed in plan and have a strong constructive solution. A pyramidal tent covers the building. Decoration of the mausoleum was made from bricks, terracotta, and stucco, and uses simple geometric forms. Figure 35 Yusuf ibn Kuseir mausoleum in Nakichivan. General view.

XII century. Every pattern has an independent motive, marked of triangular six edged polygon in form of rhombus facing blocks attached to the fundamental laying. Above the geometric patterns, we see a rounded band with arabesques with inscriptions from Quran. Only the northern part of the mausoleum have different composition.

The upper part of the portal is decorated with an epigraph. All of the epigraphs of the mausoleum are made of well-burnt bricks. Figure 36 Photo of the pattern on door decoration of Yusif ibn Kuseyir Mausoleum. It was built 26 years later than previous mausoleum. This mausoleum uses much more detailed premisses but the main principles of architecture attitudes stays the same.

We could call it a monument that represents Nakchivan architectural style of Seljuc Empire reign period. It is obvious how the architect improve his art style with the growing complexity of its multiply decorative designs and for a far greater articulation of surfaces of the walls. Photo by Javid Seyidov It is clear that mausoleums in Azerbaijan create a distinctive group, both related to, and separated from mausoleums of Anotolia and Iran.

Almost all of them have preserved the name of the architects. Nakhchivan, Azerbaijan 5. Karabakh Geometric Patterns It is important to notice one more part of territory of Azerbaijan — Karabakh. Kharabakh is a territory of Azerbaijan occupied and controlled by Armenia. Several Islamic architectural monuments have been damaged. The fact is that the destruction still is — and will continue to be- an obstacle to study those architectural monuments, since even general information and old documentation about those monuments is difficult to obtain.

Shusha Shusha is the one of the most important cities in Nakhorno-Karabakh region. Having obtained relative political and economic independence in the dismembered country, khans first of all tried to build capitals with strong defense, stable economy and beautiful urban environment. Though most of the capitals were old, there were new cities, their emergence due to historical and natural factors. The founder of the Karabakh Khanate took up building a reliable residence for himself after gaining independence in The Shusha summer pasture was chosen for the location of the new residence place.

This stone inscription had been taken off during the following reconstruction. According to this lost inscription, Shusha Castle was founded in Most buildings of Shusha were two-floor and quarry-stone. With stained-glass windows shebeke of their big verandas and multicolored decorations, Shusha's traditional houses did not differ from those of other Azerbaijan regions.

Several valuable specimens of those houses have survived. However, most of them have not survived. Besides houses, each Shusha neighborhood was formed by a local socio- religious center. Such centers consisted of buildings around a neighborhood square, a mosque, madrasa, bath, shop and spring. Neighborhood mosques Chol Gala, Taza, Saatli, and Mamayi with athree-nave prayer hall are notable for the special perfection of their plan and location.

While most of neighborhood mosques have small booths for muezzins on their roofs, the Saatii Mosque has a brick minaret with patterned decoration. The prayer hall of the mosque is three-nave, almost a square meters. From the northern part, a three-beam veranda makes the Juma Mosque a rectangle The hall is divided into naves by 6 stone columns. While the side sections are under pointed coverage, the two square parts are domed. The interior is lighted through double windows. The entire building from stone, the minarets are of bricks.

The cylindric bodies of the minarets have horizontal belts, and each section is laid on by different brick patterns. This mosque, built by Kerbalayi Sefi Khan in , looks likethe juma mosques of Aghdam and Shusha in terms of general plan-and-location specifics. However, the two minarets of the Ashaghi Govhar Aga are placed not in the front facade, but in the corners of the rear one.

Islamic geometric patterns

Founded by the Garabakh Khan Panahali years ago in place of an ancient settlement, Shusha is a rarity of Azerbaijan medieval urban development, a live encyclopedia of Garabakh architecture. Stained-glass window shebeke. By this inscription, the tomb was finished on July 15th, Aghdam, Karabakh, Azerbaijan. The nine sides of the body have beams, while the northern, eastern and western sides have door and window frames arranged. Because of a large size and artistic concept, the northern frame is the main entry.

The top pointed segments of all niches, doors and windows in the tomb body have been processed through subtle stalactite compositions. Fine pilasters, to an extent seeming too small for stone architecture, were constructed in the body corner. Besides stalactites, facade surfaces are decorated with stone carvings and different symbolic animals bulls, lions, deer, rabbits, etc.

For live appearance on the natural stone, these pictures were dark-red- painted. The tomb has dynamic volume composition, which is typical for Azerbaijan tower-shaped tombs. However, the original features of Aran, including Karabakh, architecture found themselves in both the construction technique and artistic decisions of this site.

Showcase: The art of Islamic patterns

The tomb has a double constitution of the under vault and over ground chamber. The both of them are cruciform. Unlike the severe and simple looking vault, the interior of the top chamber is extremely luxurious. The square central part of the interior covering and beam sections joining it from the North and South have complicated and subtle stalactites. The south wall, facing the front door, is like a richly decorated mehrab. Historical review The actual Portuguese territory was under the rule of Muslims during more than five centuries, between the eighth-century until the thirteenth-century.

During this period, Christian, Jews, and Muslims lived side by side and had freedom of cult. Consequently, this cross-cultural relationship fostered and enhanced the flourishing of new ideas and concepts. Being deeply rooted in the essence of the populations of these regions, lasting until the present. But not only here, but also in other southern regions of Portugal we can find traces of the Islamic inheritance, manly in Alentejo and also in Estremadura.

ISBN 10: 9810217048

Vincent were kept, later to be taken to Lisbon in the 12th century… This is quite an original circumstance that we witness in Portugal —but also in Spain. Mozarabic art 8thth century was influenced by the centers of political power in Iberia such as Toledo, Cordoba and Seville under the realms of the emirates and the caliphate Nevertheless, on the other hand, one could find, also, entire communities of muladis, that is to say, Christians converted to the Islam. In the Alhambra 14th C , Spain above , geometric pattern is perfectly integrated with biomorphic design arabesque and calligraphy.

These are the three distinct, but complementary, disciplines that comprise Islamic art. They form a three-fold hierarchy in which geometry is seen as foundational. This is often signified by its use on the floors or lower parts of walls, as shown in the image above. The decorative elements deployed use a range of symmetries that have now been classified as belonging to distinct mathematical groups, but the subtlety and beauty of the designs is unparallelled in modern mathematical thinking.

Islamic designers used the full range of Archimedean tilings comprised of simple polygons first discovered by the Greeks, but added to and expanded upon these with extraordinary visual and spatial ingenuity. The pattern above after Paul Marchant is based on elements of medieval designs typically found in Cairo. Notice the pattern of underlying polygons: hexagons, triangles, squares, dodecagons.

The underling tiling pattern is usually hidden beneath the final design, as if behind a veil, but the viewer is always given an intimation of the hidden order and this is part of what gives the designs their meditative power. With a compass and ruler an Iranian master craftsman demonstrates a method for setting out a pattern which employs fold radial symmetry.

Note the construction of the decagram pointed star.

Symmetries of Islamic Geometrical Patterns Symmetries of Islamic Geometrical Patterns
Symmetries of Islamic Geometrical Patterns Symmetries of Islamic Geometrical Patterns
Symmetries of Islamic Geometrical Patterns Symmetries of Islamic Geometrical Patterns
Symmetries of Islamic Geometrical Patterns Symmetries of Islamic Geometrical Patterns
Symmetries of Islamic Geometrical Patterns Symmetries of Islamic Geometrical Patterns
Symmetries of Islamic Geometrical Patterns Symmetries of Islamic Geometrical Patterns
Symmetries of Islamic Geometrical Patterns Symmetries of Islamic Geometrical Patterns
Symmetries of Islamic Geometrical Patterns Symmetries of Islamic Geometrical Patterns

Related Symmetries of Islamic Geometrical Patterns

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