Geometry in Islamic Art and Architecture. By: Sydney Griswold, Sarah Lutz, Abigail Bouldin, and Lucien Dalton

Transcription

1 Geometry in Islamic Art and Architecture By: Sydney Griswold, Sarah Lutz, Abigail Bouldin, and Lucien Dalton

2 Art

3 History of Islamic Art Began in the 7th century Includes many different fields eleven main countries and their racial/cultural history including: Spain, Iran, Egypt, Turkey, Morocco, South-East Asia, Syria, Bosnia, Uzbekistan, Azerbaijan, and India. Architecture, calligraphy, painting, ceramics, textiles, and other forms House of wisdom Not restricted to religion Islamic art includes aspects of the varied culture of Islamic societies Influenced by Greek, Roman, early Christian and Byzantine Art styles

4 Basic elements of Islamic art Themes of Islamic Art Geometry Calligraphy Arabesque interlacing and seemingly Calligraphy Geometry never ending plant floral or vegetal (plant like) designs in repetition Repeating element in Islamic Art Arabesque in Islamic art is used to represent the transcendent, indivisible, and infinite nature of God Non-figural Arabesque Believed humans in art was a sin to God and is forbidden in Quran Figural Islamic art exists, but is less common than the other types

5 Arabesque or vegetal patterns Geometric patterns

6 Calligraphy in Art Calligraphy is a very important form of art and writing in Islamic Culture Decoration of the Quran s manuscript connects art and religion Calligraphers were considered the most important artists because they revealed the word of God Calligraphic panel by Mustafa Râkim. The panel reads God, there is no god but He, the Lord of His prophet Muhammad (peace be upon him) and the Lord of all that has been created.

7 Painting and Ceramics Glazed ceramics was most prevalent between the eighth and eighteenth century A lot of ceramics during this time period where inscribed with various different inscriptions. Generally the inscriptions were carved into the ceramics (whether plates, tiles, etc.), covered with colored glazes before the final firing was done.

8 Geometric Patterns in Islamic Art Since the representation of animals or human beings were primarily forbidden in Islamic art causing them to develop these geometric patterns that appear to continue on infinitely. The four basic shapes, or repeat units, from which the more complicated patterns are constructed are: circles and interlaced circles squares or four-sided polygons the ubiquitous star pattern and multi sided polygons

9 Intersecting Circles and Square Pick radius Draw a circle with 2 intersection points on the radius Create two new intersection points using protractor Creates perpendicular line Using 4 intersection points create intersecting circles Using 8 intersection points, draw diagonal lines Connecting points, create a square

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11 Meaning of Symbols in Islam Circle One God Triangle Human and principles of Harmony Square Physical experience and physical world Star Equal radiation in all directions from a similar point Spread of Islam Hexagon Heaven

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13 Persian Girih Tiles The Girih tiling was used to decorate Islamic buildings, but its mathematical patterns were not recognized until now. Scholars had thought the girih were created by drawing zigzag lines with a straightedge and compass. But when Peter Lu (from Harvard University) saw them in 2007, he recognised the regular but non-repetitive patterns of Penrose tiling (only uses two tiles) a concept developed in the West in the 1970s. Simple periodic patterns can be created easily by repeating a unit cell of several elements, a technique widely used in tile patterns, but the rotational symmetry possible is limited.

14 Girih Tiles Girih Patterns are made from five basic tile shapes A bowtie shape Elongated Hexagon A Rhombus A pentagon A decagon

15 Moroccan Zellige Tiles The art of Zelij is founded by Morocco during the tenth century Comes from the Arabic word al zulaycha meaning little polished stone. This is because they were imitating the idea of Roman mosaics but instead of using small pieces of polished marble they used fragments of colored earthward tiles. can be written in a multitude of ways I.e. Zillij or Zelij Islam teaches that life is based on a universal cosmic intelligence Found on walls and floors of mosques, homes, public water fountains, tombs and architecture. Iis an art with a foundation in learning, discipline and faith. Islamic Zilij artist try to inspire their viewers into an appreciation of the laws that govern the universe

16 ns o i t a l l e s Tes

17 Ani m atio boo n by geo k on Eric B me Islam rou g tric i c des ign

18 Recreating the tessellation pattern in the Great Mosque of Cordoba 1. Create a circle in a square with 8 equal sections 2. Drawing four lines through the intersections not including the top and bottom intersections. Consider the lines to be two opposing v shapes. The lines do not end in the corners of the square. 3. Repeating the same process except rotate counterclockwise by 90 degrees and then draw your two opping v shaped lines. 4. With a different pen draw the red lines shown 5. Continuing, draw a four pointed star 6. Erasing non permanent lines you can tessellate your pattern in a grid of squares to create a bigger composition

19 Geometric Tessellation

20 Euclid's Elements Islamic geometry is rooted in Euclid s The Elements. We can see its influence on geometric art. The Elements was translated into Arabic in the late 8th century in the House of Wisdom. Mathematicians worked with geometric proofs in the style of Euclid s Elements, sometimes borrowing rules from it. Though, they were still more concerned with the practical applications than with the theory behind it. Craftsmen were familiar with Euclidean elements used in drawing geometric figures and shapes, for example using letters to label points. However, they did not use geometric proofs, nor had they been trained in the methods of Euclid.

21 Abu Nasr al-farabi Background Islamic mathematician, philosopher, music scholar, cosmologist, etc - a major thinker in the history of Islamic philosophy. Little is known about his life, but it is believed that al-farabi: Became known as the second master or second teacher, i.e. second only to Aristotle. Was born 870 CE in Farab, Iran. Lived in various cities including Baghdad, Iraq and Aleppo, Syria, where he taught philosophy. Died 950 CE in Damascus, Syria, killed by highway robbers. Was concerned with the practical applications of his work. Wrote the treatise A Book of Spiritual Crafts and Natural Secrets in the Details of Geometrical Figures which taught artists how to solve geometric problems.

22 Abu Nasr al-farabi A Book of Spiritual Crafts and Natural Secrets in the Details of Geometrical Figures The treatise solved the three following problems: To construct at the endpoint A of a segment AB a perpendicular to that segment, without extending the segment beyond A. To divide a line segment into any number of equal parts. To construct a square in a given circle. The three constructions can be used to make art patterns by allowing them to: Produce infinite patterns. Fit their patterns into specific areas.

23 Abu Nasr al-farabi Constructions 1. To construct at the endpoint A of a segment AB perpendicular to that segment, without extending the segment beyond A. This construction was necessary for artistic patterns such as the one pictured to the right. The artist had to create a line perpendicular to a segment, without extending the line past the segment.

24 Abu Nasr al-farabi Constructions Proof The circle that passes through points E, A and C has center at point D because DC = DA = DE. Therefore, EC is a diameter of circle EAC. So, angle EAC is an angle in a semicircle, and therefore a right angle.

25 Abu Nasr al-farabi Constructions 2. To divide a line segment into any number of equal parts. Add midpoints H and T on the perpendiculars. Join H to Z and E to T with straight lines. For example, dividing a line into 3 equal segments: Begin with line segment AB. Draw perpendiculars AE from A and BZ from B, in opposite directions, such that AE=BZ. Now AG=GD=DB.

26 Abu Nasr al-farabi Constructions Proof AHG and BTD are each right triangles, with G = D and H = T, and HA = BT. Therefore, the triangles are congruent, and AG = BD. HG and ED are parallel, so triangles AHG and AED are similar. So, AH / AG = (AH + HE) / (AG + GD). This means that AH (AG + GD) = AG (AH + HE), which is equivalent to AH (GD) = AG (HE). Because EH = AH, DG = GA.

27 Abu Nasr al-farabi Constructions Pattern using al-farabi s second construction:

28 Abu Nasr al-farabi Constructions 1. Start with equilateral triangle. 2. Divide each side into 6 equal segments. 3. Trace patterns along lines from step 2.

29 Abu Nasr al-farabi Constructions 3. To construct a square in a given circle. 1. Given circle with center S, draw a diameter ASG. 2. Create equal arcs AZ, AE, GT, and GH 3. Draw lines ZE and TH, which intersect the diameter at I and K. 4. Draw ZK and TI, which intersect at M. 5. Draw diameter through S, M. Let the endpoints be D and B. 6. Then ADGB will be a square.

30 Abu Nasr al-farabi Constructions Islamic art led to the expansion of geometric proofs, as artists wanted more constructions to work with in their designs. Mathematicians were looking for practical uses of their work. Artists or craftsmen weren t interested in math themselves, but mathematicians such as al-farabi were doing math to specifically aid artists/craftsmen. Image on right: uses constructions for how to make perpendicular lines at ends of segments and how to divide lines into equal segments.

31 Architecture

32 Calligraphy in Architecture Calligraphy is very important in Islamic Architecture as well as in Islamic art Calligraphy is important because it doesn t have any visual images. In Islam it is improper for there to be an image that can be worshipped. Most of the calligraphy that is inscribed on buildings are verses from the Quran, poems, or other inspirational pieces. On the Qutub Minar, the many inscriptions are in Parso-Arabic and Nagari characters and they reveal the history of its construction and restoration. These are Quranic inscriptions. Qutub Minar

33 Overview of Mosque Architecture Style, decoration, and layout of mosques can vary in different regions, but because of the common purpose of mosques, certain architectural features appear all of the world. Sahn (courtyard): This area has to be big enough to fit the entire male population in that area. So the mosques must also have a large prayer hall (sometimes adjoined to the courtyard). Minaret from Suleymaniye Mosque Mihrab (niche): Indicates the direction of Mecca. Minaret (tower): The call to prayer is announced from the tower. This is the most visible aspect of most mosques. Qubba (dome): A symbolic representation of the vault of heaven. The interior of the dome is usually covered with intricate geometric patterns

34 Mezquita- Mosque of Cordoba Mezquita - Mosque of Cordoba

35 Mezquita - Mosque of Cordoba The Mezquita was built by Prince Abd al-rahman. When his family was overthrown/massacred in Damascus, he fled to Spain and gained control over most of the Iberian Peninsula. Prince Abd al-rahman sponsored many architectural projects while he had control over Spain. In the prayer hall, the focal point is the mihrab which is a prayer niche. The Mihrab of the Mezquita opens to a small octagonal room covered by the dome (qubba) The scalloped dome is made from crisscrossing ribs that create pointed arches. The walls of this area rise up and the dome is surrounded by an inscription.

36 Inscriptions in the Mosque of Cordoba

37 Muqarnas Ceiling Muqarnas derived its name from Arabic ﻣﻘرﻧص, meaning stalactite vaults The construction of Muqarnas uses a system of complex mathematics : a tribute to the great mathematical achievements of Muslim scholars, as of most of Islamic decoration. Muqarnas are an architectural feature of geometric designs in 3D. The Islamic geometry were represented in small niches arranged in such fashion resembling caverns or stalactites, arranged in tiers usually under domes, Iwans, Mihrabs, Minarets, Squinches, columns, cornices and most commonly, under arches and vaults.

38 Muqarnas There are two main types of muqarnas North African/Middle Eastern Style Made using vertical triangular sections that are placed next to each other. Iranian Style Horizontal tiers are created which are then connected with others segments that connect the tiers to each other.

39 Muqarnas Ceiling Muqarnas consist of different tiers which each consist of their own cells that look like little vaults The designs of the muqarnas can be projected onto a plane because the vaults do not overlap

40 Works Cited etry-of-islamic-architecture ometry/unit5/unit5.html / html -education-between-philosophy-and-sociological-theory h/islamic_mathematics.pdf hapter/introduction-to-islamic-art/ om.htm dieval-islamic-tiling-reveals-mathematical-savvy/ m/beginners-guide-islamic-art/a/arts-of-the-islamicworld thematics-in-islamic