A kilim (Persian: گلیم gilīm; Turkish: kilim) is a flat tapestry-woven carpet or rug traditionally produced in countries of the former Persian Empire, including Iran and Turkey, but also in the Balkans and the Turkic countries.
Kilims can be purely decorative or can function as prayer rugs. Modern kilims are popular floor coverings in Western households.
Kütahya Province (Turkish: Kütahya ili) is a province in the Aegean region of Turkey. Its area is 11,634 km, and its population is 580,701 (2022). In 1990, Kütahya had a population of 578,000.
The neighboring provinces are Bursa to the northwest, Bilecik to the northeast, Eskişehir to the east, Afyon to the southeast, Usak to the south, Manisa to the southwest and Balıkesir to the west.
Semnan (Persian: سمنان; pronounced [semˈnɒːn] ) is a city in the Central District of Semnan County, Semnan province, Iran, serving as capital of the province, the county and the district. The city is on the alluvial fan of the Golrudbar creek in the north-central part of the country, 216 km east of Tehran and 640 km west of Mashhad. With a population of 185,129 people in 2016, Semnan is the hub of the Semnani language, a sub-branch of the Iranian languages spoken to the north. It is home to the Semnani ethnic group.
Semnan offers various recreational activities; historical and religious sites; festivals, gardens and parks; and centers of higher education and Semnani culture. The city is the cultural and political capital of Semnan province. The city's main souvenirs are daffodil flowers, Shirmal pastry, Kolüçe cookies, kilim rugs, and shortbread.
An oriental rug is a heavy, and craftly skilled textile that was orginally produced in certain regions of Asia called the "Orient". These oriental rugs were the first example of rugs until they grew more advanced. They have been around for a millennia close to East and Central Asia.
Oriental carpets can be pile woven or flat woven without pile, using various materials such as silk, wool, cotton, jute and animal hair. Examples range in size from pillows to large, room-sized carpets, and include carrier bags, floor coverings, decorations for animals, Islamic prayer rugs ('Jai'namaz'), Jewish Torah ark covers (parochet), and Christian altar covers. Since the High Middle Ages, oriental rugs have been an integral part of their cultures of origin, as well as of the European and, later on, the North American culture.
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. This article focuses, however, on mathematics in the visual arts.
Mathematics and art have a long historical relationship. Artists have used mathematics since the 4th century BC when the Greek sculptor Polykleitos wrote his Canon, prescribing proportions conjectured to have been based on the ratio 1:√2 for the ideal male nude. Persistent popular claims have been made for the use of the golden ratio in ancient art and architecture, without reliable evidence. In the Italian Renaissance, Luca Pacioli wrote the influential treatise De divina proportione (1509), illustrated with woodcuts by Leonardo da Vinci, on the use of the golden ratio in art. Another Italian painter, Piero della Francesca, developed Euclid's ideas on perspective in treatises such as De Prospectiva Pingendi, and in his paintings. The engraver Albrecht Dürer made many references to mathematics in his work Melencolia I. In modern times, the graphic artist M. C. Escher made intensive use of tessellation and hyperbolic geometry, with the help of the mathematician H. S. M. Coxeter, while the De Stijl movement led by Theo van Doesburg and Piet Mondrian explicitly embraced geometrical forms. Mathematics has inspired textile arts such as quilting, knitting, cross-stitch, crochet, embroidery, weaving, Turkish and other carpet-making, as well as kilim. In Islamic art, symmetries are evident in forms as varied as Persian girih and Moroccan zellige tilework, Mughal jali pierced stone screens, and widespread muqarnas vaulting.