Geometric artwork in the form of the Arabesque was not widely used in the Middle East or Mediterranean Basin until the golden age of Islam came into full bloom. During this time, ancient texts on Greek and Hellenistic mathematics as well as Indian mathematics were translated into Arabic at the House of Wisdom, an academic research institution in Baghdad. Like the later European Renaissance that followed, mathematics, science, literature and history were infused into the Islamic world with great, mostly positive repercussions.
The works of ancient scholars such as Plato, Euclid, Aryabhata and Brahmagupta 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 and times of Salah and Ramadan. Plato's ideas about the existence of a separate reality that was perfect in form and function and crystalline in character, Euclidean geometry as expounded on by Al-Abbās ibn Said al-Jawharī (ca. 800-860) in his Commentary on Euclid's Elements, the trigonometry of Aryabhata and Brahmagupta as elaborated on by Muhammad ibn Mūsā al-Khwārizmī (ca. 780-850), and the development of spherical geometry by Abū al-Wafā' al-Būzjānī (940–998) and spherical trigonometry by Al-Jayyani (989-1079) for determining the Qibla and times of Salah and Ramadan, all served as an impetus for the art form that was to become the Arabesque.
Arabesque art consists of a series of repeating geometric forms which are occasionally accompanied by calligraphy. Ettinghausen et al. describe the arabesque as a "vegetal design consisting of full...and half palmettes [as] an unending continuous pattern...in which each leaf grows out of the tip of another. To the adherents of Islam, the Arabesque are symbolic of their united faith and the way in which traditional Islamic cultures view the world.
There are two modes to arabesque art. 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). In the first mode, each repeating geometric form has a built-in symbolism ascribed to it. For example, the square, with its four equilateral sides, is symbolic of the equally important elements of nature: earth, air, fire and water. 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 forms. This mode recalls the feminine 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 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. Proverbs and complete passages from the Qur'an can be seen today in Arabesque art. The coming together of these three forms creates the Arabesque, and this is a reflection of unity arising from diversity (a basic tenet of Islam).
The arabesque can also be equally thought of as both art and science, some say. The artwork 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 Arabesque, but these forms always existed before as part of God's creation, as shown in this picture.
There is great similarity between arabesque 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 style of arabesque comes from. The reason for this is that the science and mathematics that are used to construct Arabesque artwork are universal.
Therefore, for most Muslims, the best artwork that can be created by man for use in the Mosque is artwork that displays the underlying order and unity of nature. The order and unity of the material world, they believe, is a mere ghostly approximation of the spiritual 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 sins of man.
In fact, Sufi Muslims believe that there is no distinction between the spiritual and material worlds. They also believe that the reason we cannot experience the spiritual world is that there are 'veils of concealment' that shield us from the perfection of the spiritual world. They therefore work to lift these veils, in order to become one with God while they are still on Earth. One of the ways that Sufi Muslims utilize to do this is to use the arabesque in depictions of the world.