Math 475 - UMass Math

Math 475
Geometry in Islamic art and
architecture
Jian Ma
Mustafa Ozdemir
Molly O’Neil
http://iranpoliticsclub.net/maps/images/095%20Roman-Persian%20Wars%20580%20pre-campaign%201%20Map.jpg
Background of history
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Islamic art focuses on geometry, patterns, symmetry, and calligraphy.
Properties of Islamic Patterns
○ Transcribed with Arabic Calligraphy from the Quran.
○ Invented between 900 AD and 1500 AD.
○ Decorate architecture for Muslims in a place of mostly Islamic people.
From the 8th century and 13th century was the golden age of Islam world, the House of
wisdom was built to attract famous scholars around the middle-east; each of them
contributed.
The book The Elements after 8th century was translated into Arabic in the house of
Wisdom.
(Abas Salman 2 - 6)
Islamic aniconism
Background of culture
Islam culture vehemently opposes Idol worships
This Leads to
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●
●
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Avoiding figurative images and focus heavily on geometrical patterns
No human statues
Abstract thinking : algebra and algorithm
No idol worship -> geometrical patterns -> circles and squares -> interlace and
overlap
Persian Zoomorphic Art
Arabic is the script of Quran, the
Islam bible.
But most of the arabic alphabets are
not geometrically symmetric or
reflexive, so even though
calligraphers are highly respected,
their zoomorphic art doesn’t contain
too much geometrical patterns
https://s-media-cache-ak0.pinimg.c
om/564x/8e/d6/94/8ed694b9b395d
3308184e047b5ee0f4e.jpg
Geometry
Is one of the most important elements of Islamic art. From the simple polygons and rectangles used as
framing devices to the highly complex interlaces of stars and irregular polygons.
The four basic shapes or repeated units from which the more complicated patterns are constructed are:
-circles and interlaced circles
-squares or four-sided polygons
-the star pattern ( derived from squares and triangles inscribed in a circle)
-multisided polygons
In Islam,
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The circle emphasizes one God.
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The triangle symbolises human and the principles of harmony.
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The square is the symbol of physical experience and the physical world.
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The star symbolizes equal radiation in all directions from a central point. Also the spread of Islam.
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The hexagon represents Heaven.
http://www.salaam.co.uk/themeofthemonth/march02_index.php?l=3
Girih Tiles
Peter J. Lu
●
was born in Cleveland, Ohio in 1978.
●
is a post-doctoral research fellow in the
Department of Physics and the School of
Engineering and Applied Sciences at
Harvard University in Cambridge,
Massachusetts.
●
He has been recognized for his discoveries
of girih tiles, quasicrystal patterns in
medieval Islamic architecture, early
precision compound machines in ancient
China, and man's first use of diamond in
neolithic China.
Darb-i Imam Shrine, Isfahan, Iran (1453)
Abdullah Khan Madrasah, Bukhara, Uzbekistan (1590)
http://www.peterlu.org/content/decagonal-and-quasicrystalline-tilings-medieval-islamic-architecture
Abdullah Khan Madrasah, Bukhara, Uzbekistan (1567)
Mir Arab Madrasah, Bukhara, Uzbekistan (1536)
http://www.peterlu.org/content/decagonal-and-quasicrystalline-tilings-medieval-islamic-architecture
Topkapi Scroll, Istanbul, Turkey
http://islamic-arts.org/2012/tiles-of-infinity/
BOWTIE
HEXAGON
RHOMBUS
PENTAGON
DECAGON
http://islamic-arts.org/2012/tiles-of-infinity/
the Abbasid al-Mustansiriyya Madrasa in Baghdad, Iraq.(1227)
Green Mosque in Bursa, Turkey. (1424)
Islamic Center of Washington (1954)
Jameh Mosque, Isfahan, Iran
http://www.gettyimages.com/detail/photo/islamic-tiling-detail-on-the-interior-walls-high-res-stock-photography/148642044
Architecture
Mosques
Hypostyle
https://i0.wp.com/www.traveli
ngthruhistory.com/wp-conten
t/uploads/2014/12/The-Great
-Mosque-of-Cordoba.jpg
Great Mosque of Cordoba
(784 Spain)
(Ettinghausen and Grabar 258)
https://www.ruralidays.com/blog/wp-content/uploads/2016/09/La-Mosqu%C3%
A9e-Cath%C3%A9drale-de-Cordoue.jpg
Four Iwan
Plan
https://classconnection.s3.amazonaws.com/815/flas
hcards/923815/jpg/picture281324161414427.jpg
Great Mosque of Isfahan
(1000 - 1200 Iran)
(Ettinghausen and Grabar 258)
https://classconnection.s3.amazonaws.com/277
/flashcards/2375277/jpeg/05d_isfahan_shah_a
erial_ha_sooimg5731355070073610.jpeg
Central Plan
Selimiye Mosque (1569 - 1575 Turkey)
https://ka-perseus-images.s3.amazonaws.com/174a566a0d24e7d6ed9223ba9811029e375d
789f.jpg
(Ettinghausen
and Grabar 269)
Mausoleums
Kharraqan mausoleum (1067 Iran)
https://upload.wikimedia.org/wikipedia/commons/b/
bd/Kharaghan.jpg
http://eurasia.travel/files/mausoleum_of_sultan_sanjar_1000x667_tl3.jpg
Mausoleum of Sultan Sanjar (1157 Central Asia)
http://archaeologydataservice.ac.uk/archives/view/
merv_ahrc_2008/images.cfm?imageType=photos
&sn=1961&CFID=573996&CFTOKEN=39545028
http://eurasia.travel/f
iles/mausoleum_of_
sultan_sanjar_720x
474_hbn.jpg
Domes
Dome of the Rock (691 Jerusalem)
https://c1.staticflickr.com/8/7126/7590544272_fe4d217c99_b.jpg
http://3.bp.blogspot.com/-qx7s-DQtODY/V
afftTUVj5I/AAAAAAAAE8E/jtFkRfUAohI/s
1600/Slide1.JPG
http://travelchannel.sndimg.com/content/da
m/images/travel/fullset/2013/11/05/3f/Domeof-the-Rock.rend.tccom.966.544.jpeg
Cupolas
http://tylerhansen.me/markreynolds/wpcontent/uploads/2010/12/1.10.jpg
Leonardo Da Vinci Cathedral Sketches
http://www.leonardodavinci.net/images/d
rawings/study-of-a-central-church.jpg
https://classconnection.s3.amaz
onaws.com/899/flashcards/1896
899/jpg/da_vinci_project_for_a_
church1348422995175.jpg
Muqarnas
http://1.bp.blogspot.com/
-I9tO8G1ppNA/VlghCNt
MecI/AAAAAAAAGEE/U
QNnlPF06ZE/s640/m7.p
ng
(Hamekasi, N., FF
Samavati, and A.
Nasri)
Isfahan, Iran
Sheikh Lotf Allah Mosque
http://gashtatour.com
/wp-content/uploads/
2016/05/Sheikh-Lotfo
llah-14.jpg
Topkapi Scroll
http://kilyos.ee.bilkent.edu.tr/~history/Pictures2/Yeni/p297.JPG
https://upload.wikimedia.org/wikipedia/com
mons/c/c0/Topkapi_Scroll_p294.JPG
https://s-media-cache-ak0.pi
nimg.com/736x/df/b7/55/dfb
7551ce744d89f880e23d9d1
c253f1.jpg
http://www.shiro1000.jp/muqarnas/img/isfahan1.gif
Bibliography
Patterns., Amazing, and www.mathforum.org/sketc. Girih Tiling Patterns in Google SketchUp (n.d.): n. pag. Web.
"Tiles of Infinity « Islamic Arts and Architecture." Islamic Arts and Architecture. N.p., n.d. Web. 26 Mar. 2017. <http://islamic-arts.org/2012/tiles-of-infinity/>.
“Islam Origins, Islam History, Islam Beliefs - Patheos” Islam History , http://www.patheos.com/Library/Islam
Dancing Person, https://images.fineartamerica.com/images-medium-large/the-persian-dancer-raiyan-talkhani.jpg
Rehmeyer, Julie. "Ancient Islamic Penrose Tiles." Science News. N.p., 23 Sept. 2013. Web. 26 Mar. 2017. <https://www.sciencenews.org/article/ancient-islamic-penrose-tiles-0>.
"Saudi Aramco World : The Tiles of Infinity." AramcoWorld. N.p., n.d. Web. 26 Mar. 2017. <http://archive.aramcoworld.com/issue/200905/the.tiles.of.infinity.htm>.
"Decagonal and Quasicrystalline Tilings in Medieval Islamic Architecture." Decagonal and Quasicrystalline Tilings in Medieval Islamic Architecture. N.p., 30 Jan. 2013. Web. 26 Mar.
2017. <http://peterlu.org/content/decagonal-and-quasicrystalline-tilings-medieval-islamic-architecture>.
Broug, Eric. Islamic Geometric Patterns. London: Thames and Hudson, 2014. Print.
Ettinghausen, Richard, and Oleg Grabar. The Art and Architecture of Islam: 650-1250. London: Penguin, 1991. Print.
Hamekasi, N., FF Samavati, and A. Nasri. "Interactive Modeling of Muqarnas." ACM Digital Library. ACM, 2011. Web. 23 Mar. 2017.
Necipoglu, Gulru. "Geometric Design in Timurid/Turkmen Architectural Practice: Thoughts on a Recently Discovered Scroll and Its Late Gothic Parallels." Archnet.
Harvard University, n.d. Web. 23 Mar. 2017.
Petersen, Andrew. Dictionary of Islamic Architecture. London: Routledge, 1996. Internet resource.
Tabbaa, Yasser. “The Muqarnas Dome: Its Origin and Meaning.” Muqarnas, vol. 3, 1985, pp. 61–74., www.jstor.org/stable/1523084.

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