Islamic geometric patterns
Encyclopedia
Islamic decoration makes great use of geometric patterns which have developed over the centuries. Many of these derived from various earlier cultures: Greek, Roman, Byzantine
Byzantine
Byzantine usually refers to the Roman Empire during the Middle Ages.Byzantine may also refer to:* A citizen of the Byzantine Empire, or native Greek during the Middle Ages...

, Central Asia
Central Asia
Central Asia is a core region of the Asian continent from the Caspian Sea in the west, China in the east, Afghanistan in the south, and Russia in the north...

n, and Persian. They are usually distinguished from the arabesque
Arabesque
The arabesque is a form of artistic decoration consisting of "surface decorations based on rhythmic linear patterns of scrolling and interlacing foliage, tendrils" or plain lines, often combined with other elements...

, the term for decoration in Islamic art
Islamic art
Islamic art encompasses the visual arts produced from the 7th century onwards by people who lived within the territory that was inhabited by or ruled by culturally Islamic populations...

 based on curving and branching vegetal forms. But sometimes foliage and linear geometric patterns are combined in a single design, and some purely abstract linear patterns adopt designs that seem clearly derived from vegetal arabesque ones. The geometric designs have evolved into beautiful and highly complex patterns, still used in many modern day settings.

The square and rectangle play a significant role in Islamic architecture. Some of the reason for this is façades built from rectangular bricks. This ornamental brickwork casts shadows in the strong desert sunlight and creates a three-dimensional effect. A reccurring motif is a small central square turned 45 degrees within a larger square. Another source for the square motif is woven baskets.

The Persianate
Persianate
A Persianate/Persified society is a society that is either based on, or strongly influenced by the Persian language, culture, literature, art, and/or identity....

 world is the main area with buildings with decorative brickwork, especially during the Seljik period; the Great Mosque of Cordoba is another example further west. The eight-pointed star is another common motif in Islamic architecture
Islamic architecture
Islamic architecture encompasses a wide range of both secular and religious styles from the foundation of Islam to the present day, influencing the design and construction of buildings and structures in Islamic culture....

, often found in tile
Tile
A tile is a manufactured piece of hard-wearing material such as ceramic, stone, metal, or even glass. Tiles are generally used for covering roofs, floors, walls, showers, or other objects such as tabletops...

-work and other media. Star patterns are extremely complex when the outer points are joined together and other intersections connect in a systematic way. The Alhambra
Alhambra
The Alhambra , the complete form of which was Calat Alhambra , is a palace and fortress complex located in the Granada, Andalusia, Spain...

 palace in Granada, Spain is a famous example of repeating motifs which occur in the tile and stucco decoration. Octagons appear in Islamic architecture in various shapes. They frequently occur in marble floors. The Citadel of Aleppo
Aleppo
Aleppo is the largest city in Syria and the capital of Aleppo Governorate, the most populous Syrian governorate. With an official population of 2,301,570 , expanding to over 2.5 million in the metropolitan area, it is also one of the largest cities in the Levant...

 in Syria
Syria
Syria , officially the Syrian Arab Republic , is a country in Western Asia, bordering Lebanon and the Mediterranean Sea to the West, Turkey to the north, Iraq to the east, Jordan to the south, and Israel to the southwest....

 contains marble opus sectile
Opus sectile
Opus sectile refers to an art technique popularized in the ancient and medieval Roman world where materials were cut and inlaid into walls and floors to make a picture or pattern. Common materials were marble, mother of pearl, and glass. The materials were cut in thin pieces, polished, then trimmed...

floors, which utilize the square and the eight-pointed star. Pierced screens (jali
Jali
A jali is the term for a perforated stone or latticed screen, usually with an ornamental pattern constructed through the use of calligraphy and geometry. Early work was performed by carving into stone, while the later more elegant used by the Mughals employed the technique of inlay, using marble...

in India]] are another common location for geometric decoration.

Significance in Islam

The arabesques and geometric patterns of Islamic art are often said to arise from the Islam
Islam
Islam . The most common are and .   : Arabic pronunciation varies regionally. The first vowel ranges from ~~. The second vowel ranges from ~~~...

ic view of the world. To Muslim
Muslim
A Muslim, also spelled Moslem, is an adherent of Islam, a monotheistic, Abrahamic religion based on the Quran, which Muslims consider the verbatim word of God as revealed to prophet Muhammad. "Muslim" is the Arabic term for "submitter" .Muslims believe that God is one and incomparable...

s, these forms, taken together, constitute an infinite pattern that extends beyond the visible material world. To many in the Islamic world, they concretely symbolize the infinite, and therefore uncentralized, nature of the creation of the one God (Allah
Allah
Allah is a word for God used in the context of Islam. In Arabic, the word means simply "God". It is used primarily by Muslims and Bahá'ís, and often, albeit not exclusively, used by Arabic-speaking Eastern Catholic Christians, Maltese Roman Catholics, Eastern Orthodox Christians, Mizrahi Jews and...

) and convey a spirituality without the figurative iconography
Iconography
Iconography is the branch of art history which studies the identification, description, and the interpretation of the content of images. The word iconography literally means "image writing", and comes from the Greek "image" and "to write". A secondary meaning is the painting of icons in the...

 of the art of other religions.

Mistakes in repetitions may be intentionally introduced as a show of humility by artists who believe only Allah can produce perfection, although this theory is disputed.
Repeating geometric forms are often accompanied by calligraphy
Calligraphy
Calligraphy is a type of visual art. It is often called the art of fancy lettering . A contemporary definition of calligraphic practice is "the art of giving form to signs in an expressive, harmonious and skillful manner"...

. Ettinghausen et al. describe the arabesque as a "vegetal design consisting of full...and half palmette
Palmette
The palmette is a motif in decorative art which, in its most characteristic expression, resembles the fan-shaped leaves of a palm tree. It has an extremely long history, originating in Ancient Egypt with a subsequent development through the art of most of Eurasia, often in forms that bear...

s [as] an unending continuous pattern...in which each leaf grows out of the tip of another." To the adherents of Islam
Islam
Islam . The most common are and .   : Arabic pronunciation varies regionally. The first vowel ranges from ~~. The second vowel ranges from ~~~...

, the continuous patterns are symbolic of their united faith and the way in which traditional Islamic cultures view the world.

There are two modes to Islamic decoration. The first recalls the principles that govern the order of the world. These principles include the bare basics of what makes objects structurally sound and, by extension, beautiful (i.e. the angle and the fixed/static shapes that it creates—esp. the truss
Truss
In architecture and structural engineering, a truss is a structure comprising one or more triangular units constructed with straight members whose ends are connected at joints referred to as nodes. External forces and reactions to those forces are considered to act only at the nodes and result in...

). In the first mode, each repeating geometric form has a built-in symbolism ascribed to it. For example, the square, with its four equilateral
Equilateral
In geometry, an equilateral polygon is a polygon which has all sides of the same length.For instance, an equilateral triangle is a triangle of equal edge lengths...

 sides, is symbolic of the equally important elements of nature: earth
Soil
Soil is a natural body consisting of layers of mineral constituents of variable thicknesses, which differ from the parent materials in their morphological, physical, chemical, and mineralogical characteristics...

, air, fire
Fire
Fire is the rapid oxidation of a material in the chemical process of combustion, releasing heat, light, and various reaction products. Slower oxidative processes like rusting or digestion are not included by this definition....

 and water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

. Without any one of the four, the physical world, represented by a circle that inscribes the square, would collapse upon itself and cease to exist. The second mode is based upon the flowing nature of plant
Plant
Plants are living organisms belonging to the kingdom Plantae. Precise definitions of the kingdom vary, but as the term is used here, plants include familiar organisms such as trees, flowers, herbs, bushes, grasses, vines, ferns, mosses, and green algae. The group is also called green plants or...

 forms. This mode recalls the feminine
Female
Female is the sex of an organism, or a part of an organism, which produces non-mobile ova .- Defining characteristics :The ova are defined as the larger gametes in a heterogamous reproduction system, while the smaller, usually motile gamete, the spermatozoon, is produced by the male...

 nature of life giving. In addition, upon inspection of the many examples of Arabesque art, some would argue that there is in fact a third mode, the mode of Arabic calligraphy.

Instead of recalling something related to the 'True Reality' (the reality of the spiritual world), for the Muslim calligraphy
Calligraphy
Calligraphy is a type of visual art. It is often called the art of fancy lettering . A contemporary definition of calligraphic practice is "the art of giving form to signs in an expressive, harmonious and skillful manner"...

 is a visible expression of the highest art of all; the art of the spoken word (the transmittal of thoughts and of history). In Islam, the most important document to be transmitted orally is, of course, the Qur'an
Qur'an
The Quran , also transliterated Qur'an, Koran, Alcoran, Qur’ān, Coran, Kuran, and al-Qur’ān, is the central religious text of Islam, which Muslims consider the verbatim word of God . It is regarded widely as the finest piece of literature in the Arabic language...

. Proverb
Proverb
A proverb is a simple and concrete saying popularly known and repeated, which expresses a truth, based on common sense or the practical experience of humanity. They are often metaphorical. A proverb that describes a basic rule of conduct may also be known as a maxim...

s and complete passages from the Qur'an can be seen. The coming together of these three forms creates the totality of Islamic decoration, and this is a reflection of unity arising from diversity (a basic tenet of Islam).

The geometric patterns can also be equally thought of as both art
Art
Art is the product or process of deliberately arranging items in a way that influences and affects one or more of the senses, emotions, and intellect....

 and science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

, some say. The art is at the same time mathematically precise, aesthetically pleasing, and symbolic. So due to this duality of creation, they say, the artistic part of this equation can be further subdivided into both secular and religious artwork. However, for many Muslims there is no distinction; all forms of art, the natural world, mathematics and science are all creations of God and therefore are reflections of the same thing - that is, God's will expressed through His Creation. In other words, man can discover the geometric forms that constitute the design, but these forms always existed before as part of God's creation, as shown in this picture.

There is great similarity between artwork from very different geographic regions. In fact, the similarities are so pronounced, that it is sometimes difficult for experts to tell where a given piece comes from. The reason for this is the rapid communication of new styles within the Iaslamic world, especially in the early period, and that the science and mathematics that are used to construct geometric art are universal. Therefore, for most Muslims, the best art that can be created by man for use in the Mosque
Mosque
A mosque is a place of worship for followers of Islam. The word is likely to have entered the English language through French , from Portuguese , from Spanish , and from Berber , ultimately originating in — . The Arabic word masjid literally means a place of prostration...

 is art that displays the underlying order and unity of nature. The order and unity of the material world, they believe, is a mere ghost
Ghost
In traditional belief and fiction, a ghost is the soul or spirit of a deceased person or animal that can appear, in visible form or other manifestation, to the living. Descriptions of the apparition of ghosts vary widely from an invisible presence to translucent or barely visible wispy shapes, to...

ly approximation of the spirit
Spirit
The English word spirit has many differing meanings and connotations, most of them relating to a non-corporeal substance contrasted with the material body.The spirit of a living thing usually refers to or explains its consciousness.The notions of a person's "spirit" and "soul" often also overlap,...

ual world, which for many Muslims is the place where the only true reality exists. Discovered geometric forms, therefore, exemplify this perfect reality because God's creation has been obscured by the sin
Sin
In religion, sin is the violation or deviation of an eternal divine law or standard. The term sin may also refer to the state of having committed such a violation. Christians believe the moral code of conduct is decreed by God In religion, sin (also called peccancy) is the violation or deviation...

s of man.

Islamic Mathematics

During the golden age of Islam
Islamic Golden Age
During the Islamic Golden Age philosophers, scientists and engineers of the Islamic world contributed enormously to technology and culture, both by preserving earlier traditions and by adding their own inventions and innovations...

, ancient texts on Greek and Hellenistic mathematics
Greek mathematics
Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 7th century BC to the 4th century AD around the Eastern shores of the Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean, from Italy to...

 as well as Indian mathematics
Indian mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics , important contributions were made by scholars like Aryabhata, Brahmagupta, and Bhaskara II. The decimal number system in use today was first...

 were translated into Arabic
Arabic language
Arabic is a name applied to the descendants of the Classical Arabic language of the 6th century AD, used most prominently in the Quran, the Islamic Holy Book...

 at the House of Wisdom
House of Wisdom
The House of Wisdom was a library and translation institute established in Abbassid-era Baghdad, Iraq. It was a key institution in the Translation Movement and considered to have been a major intellectual centre during the Islamic Golden Age...

, an academic research institution in Baghdad
Baghdad
Baghdad is the capital of Iraq, as well as the coterminous Baghdad Governorate. The population of Baghdad in 2011 is approximately 7,216,040...

. The works of ancient scholars such as Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...

, Euclid
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...

, Aryabhata
Aryabhata
Aryabhata was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy...

 and Brahmagupta
Brahmagupta
Brahmagupta was an Indian mathematician and astronomer who wrote many important works on mathematics and astronomy. His best known work is the Brāhmasphuṭasiddhānta , written in 628 in Bhinmal...

 were widely read among the literate and further advanced in order to solve mathematical problems which arose due to the Islamic requirements of determining the Qibla
Qibla
The Qiblah , also transliterated as Qibla, Kiblah or Kibla, is the direction that should be faced when a Muslim prays during salah...

 and times of Salah and Ramadan
Ramadan
Ramadan is the ninth month of the Islamic calendar, which lasts 29 or 30 days. It is the Islamic month of fasting, in which participating Muslims refrain from eating, drinking, smoking and sex during daylight hours and is intended to teach Muslims about patience, spirituality, humility and...

. Plato's ideas about the existence of a separate reality that was perfect in form and function and crystalline in character, Euclidean geometry
Euclidean geometry
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...

 as expounded on by Al-Abbās ibn Said al-Jawharī (ca. 800-860) in his Commentary on Euclid's Elements, the trigonometry
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...

 of Aryabhata and Brahmagupta as elaborated on by the Persian
Persian people
The Persian people are part of the Iranian peoples who speak the modern Persian language and closely akin Iranian dialects and languages. The origin of the ethnic Iranian/Persian peoples are traced to the Ancient Iranian peoples, who were part of the ancient Indo-Iranians and themselves part of...

 mathematician Khwārizmī (ca. 780-850), and the development of spherical geometry
Spherical geometry
Spherical geometry is the geometry of the two-dimensional surface of a sphere. It is an example of a geometry which is not Euclidean. Two practical applications of the principles of spherical geometry are to navigation and astronomy....

 by Abū al-Wafā' al-Būzjānī (940–998) and spherical trigonometry
Spherical trigonometry
Spherical trigonometry is a branch of spherical geometry which deals with polygons on the sphere and the relationships between the sides and the angles...

 by Al-Jayyani
Al-Jayyani
Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī was a mathematician, Islamic scholar, and Qadi from Al-Andalus...

 (989-1079) for determining the Qibla
Qibla
The Qiblah , also transliterated as Qibla, Kiblah or Kibla, is the direction that should be faced when a Muslim prays during salah...

 and times of Salah and Ramadan
Ramadan
Ramadan is the ninth month of the Islamic calendar, which lasts 29 or 30 days. It is the Islamic month of fasting, in which participating Muslims refrain from eating, drinking, smoking and sex during daylight hours and is intended to teach Muslims about patience, spirituality, humility and...

, all served as an impetus for geometric patterns in Islamic art
Islamic art
Islamic art encompasses the visual arts produced from the 7th century onwards by people who lived within the territory that was inhabited by or ruled by culturally Islamic populations...

.
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