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an endpoint at A; other endpoints are the intersections of the four rays with the two sides of BC and DC of rectangle ABCD. Then, find the midpoint of the fourth segment created from the fourth ray point E. Construct an arc with center A and radius AE to intersect AB at point F and the second ray at point G. The second segment is now a part of the rectangle's diagonal. Make a line parallel to AD and passing through point G that intersects the first ray at point H and the third ray at point I. The line HF passes through point E and intersects the third ray at L and line AD at J. Construct a line passing through J that is parallel to the third ray. Also construct line EI and find M which is the intersection of this line with AD. From the point F make a parallel line to the third ray to meet the first ray at K. Construct segments GK, GL, and EM. Find the point N such that GI = IN by constructing a circle with center I and radius IG. Construct the line DN which is parallel to GK to intersect the line emanating from J, and find P to complete the regular pentagon EINPJ. Line DN meets the perpendicular bisector of AB at Q. From Q construct a line parallel to FK to intersect ray MI at R. As shown in the figure, using O which is the center of the rectangle ABCD as a center of rotation for 180°, one can make the fundamental region for the tiling.
505:
higher social and economic status the owner is more likely to have. A good example of this is Azad Koliji, a
Dowlatabad Garden in Iran . The girih patterns on its window successfully demonstrate multiple layers. The first layer would be the actual garden, of which people can have a glimpse when they open the window. Then there is the first girih pattern on the outside of the window, the carved pattern. Another artificial layer is represented by the colorful glass of the window, whose multicolored layers create the sense of a mass of flowers. This abstract layer forms a clear contradiction with the real layer outside the window, and gives the space for the imagination.
448:
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304:, meaning "knot". In most cases, only the girih (and other minor decorations like flowers) are visible rather than the boundaries of the tiles themselves. The girih are piece-wise straight lines that cross the boundaries of the tiles at the center of an edge at 54° (3π/10 radians) to the edge. Two intersecting girih cross each edge of a tile. Most tiles have a unique pattern of girih inside the tile that are continuous and follow the symmetry of the tile. However, the decagon has two possible girih patterns one of which has only fivefold rather than tenfold rotational symmetry.
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three-dimensional projections. Drawings such as shown on this scroll would have served as pattern-books for the artisans who fabricated the tiles, and the shapes of the girih tiles dictated how they could be combined into large patterns. In this way, craftsmen could make highly complex designs without resorting to mathematics and without necessarily understanding their underlying principles.
1100:
2012:
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First, divide the right angle A into five parts of the same degree by creating four rays that start from A. Find an arbitrary point C on the second ray and drop perpendiculars from C to the sides of angle A counterclockwise. This step creates the rectangle ABCD along with four segments that each have
346:
in
Istanbul, the administrative center of the Ottoman Empire, and believed to date from the late 15th century, the scroll shows a succession of two- and three-dimensional geometric patterns. There is no text, but there is a grid pattern and color-coding used to highlight symmetries and distinguish
337:
This finding was supported both by analysis of patterns on surviving structures, and by examination of 15th-century
Persian scrolls. There is no indication of how much more the architects may have known about the mathematics involved. It is generally believed that such designs were constructed by
504:
The girih has been widely applied on architecture. Girih on
Persian geometric windows meet the requirements of Persian architecture. The specific types of embellishments utilized in orosi typically linked the windows to the patron's social and political eminence. The more ornate a window is, the
404:
First, divide the right angle into five congruent angles. An arbitrary point P is selected on the first ray counterclockwise. For the radius of the circle inscribed in the decagram, one half of the segment created from the third ray, segment AM, is selected. The following figure illustrates a
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step-by-step compass-straightedge visual solution to the problem by the author. Note that the way to divide a right angle into five congruent angles is not a part of the instructions provided, because it is considered an elementary step for designers.
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artisans. Designers of both styles were concerned with using their inventories of geometrical shapes to create the maximum diversity of forms. This demanded a skill and practice very different from mathematics.
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251:). All of them except the pentagon have bilateral (reflection) symmetry through two perpendicular lines. Some have additional symmetries. Specifically, the decagon has tenfold
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This use of repeating patterns created from a limited number of geometric shapes available to craftsmen of the day is similar to the practice of contemporary
European
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271:. By 13th century, the Islamic discovered a new way to construct the “tile mosaic” due to the development of arithmetic calculation and geometry—the girih tiles.
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drafting zigzag outlines with only a straightedge and a compass. Templates found on scrolls such as the 97-foot (29.5 metres) long
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Sarhangi, Reza (2012). "Interlocking Star
Polygons in Persian Architecture: The Special Case of the Decagram in Mosaic Designs".
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Peter J. Lu and Paul J. Steinhardt (2007). "Decagonal and Quasi-crystalline
Tilings in Medieval Islamic Architecture".
84:. They have been used since about the year 1200 and their arrangements found significant improvement starting with the
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Lu, P. J.; Steinhardt, P. J. (2007). "Decagonal and Quasi-Crystalline
Tilings in Medieval Islamic Architecture".
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All sides of these figures have the same length, and all their angles are multiples of 36° (π/5
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Complex girih patterns with 16-, 10- and 8-point stars at different scales in ceiling of the
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255:(rotation by 36°); and the pentagon has fivefold rotational symmetry (rotation by 72°).
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Geometric construction of a tessellation from Mirza Akbar architectural scrolls
292:) that decorate the tiles. The tiles are used to form girih patterns, from the
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By the late 11th century, the
Islamic artists in North Africa start to use “
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2011:
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461:, Turkey, with 6-point stars; the surrounds have floral arabesque tiling
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Geometric construction of an interlocking decagram-polygon mosaic design
19:
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Interior archway at the opening of the Sultan's Lodge in the
Ottoman
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Step-by-step compass-straightedge construction of the tessellation
407:
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382:
374:
366:
285:
280:
76:
41:
29:
18:
840:"Medieval Islamic architecture presages 20th century mathematics"
799:"Built on Light: The 'Crafty' Art of Geometric Patterned Windows"
784:
The Topkapi Scroll: Geometry and Ornament in Islamic Architecture
4166:
Viewpoints: Mathematical Perspective and Fractal Geometry in Art
3281:
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2461:
2237:
2232:
1865:
1824:
1610:
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1441:
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320:
suggested that girih tilings possess properties consistent with
93:
63:
46:
Construction lines are usually hidden: geometric tiles on left,
3049:
2043:
872:
2039:
855:"Medieval Islamic tiling reveals mathematical savvy"
4221:
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1107:
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4063:The Drawing of Geometric Patterns in Saracenic Art
481:, Turkey (1424), with 10-point stars and pentagons
4198:Goudreau Museum of Mathematics in Art and Science
453:A window of the crown prince's apartment in the
2981:Islamic world contributions to Medieval Europe
685:Sebastian R. Prange (September–October 2009).
395:An interlocking decagram-polygon mosaic design
387:An interlocking decagram-polygon mosaic design
379:An interlocking decagram-polygon mosaic design
371:An interlocking decagram-polygon mosaic design
4193:European Society for Mathematics and the Arts
3367:Mathematica: A World of Numbers... and Beyond
3061:
2055:
884:
803:International Journal of Islamic Architecture
297:
8:
3347:List of works designed with the golden ratio
605:. Potsdam : H.F. Ullmann. p. 448.
3832:
3456:
3068:
3054:
3046:
2965:Islamic Art: Mirror of the Invisible World
2577:
2304:
2083:
2062:
2048:
2040:
1648:
1074:
891:
877:
869:
110:
3407:Cathedral of Saint Mary of the Assumption
814:
777:
775:
601:Hattstein /Delius., Markus/Peter (2013).
16:Five tiles used in Islamic decorative art
3018:Oriental carpets in Renaissance painting
842:. Harvard University Gazette. 2007-02-22
104:The five shapes of the tiles, and their
3953:Vier Bücher von Menschlicher Proportion
2938:Heaven on Earth: Art from Islamic Lands
553:
420:
342:may have been consulted. Found in the
7:
561:
559:
557:
334:, predating them by five centuries.
4138:Journal of Mathematics and the Arts
2945:Hajj: Journey to the Heart of Islam
4152:Making Mathematics with Needlework
1927:Influences on Western architecture
66:that were used in the creation of
14:
3978:I quattro libri dell'architettura
2846:Museum for Islamic Art, Jerusalem
603:Islam : art and architecture
80:) for decoration of buildings in
4257:
4256:
3502:Self-portrait in a Convex Mirror
3186:
2291:
2023:
2010:
1098:
486:
466:
446:
426:
1896:Aga Khan Award for Architecture
834:Patterns in Arabic Architecture
267:”, which is the predecessor of
4285:Islamic architectural elements
4213:National Museum of Mathematics
3965:Regole generali d'architettura
1:
159:elongated (irregular convex)
3738:Garden of Cosmic Speculation
3003:Mathematics and architecture
1988:Sudano-Sahelian architecture
308:Mathematics of girih tilings
259:The emergence of girih tiles
857:. New Scientist. 2007-02-22
786:. Getty Research Institute.
4331:
3255:Islamic geometric patterns
1356:Islamic geometric patterns
278:
68:Islamic geometric patterns
4252:
4076:A Mathematician's Apology
3184:
2986:Influences on Western art
2289:
2001:
1790:Dar al-Shifa (Bimaristan)
1096:
816:10.1007/s00004-016-0288-6
580:10.1007/s00004-012-0117-5
298:
4188:The Bridges Organization
1906:Museum with No Frontiers
782:Gulru Necipoglu (1995).
312:In 2007, the physicists
4050:The Grammar of Ornament
4002:Nature's Harmonic Unity
3912:De prospectiva pingendi
2017:Architecture portal
797:Koliji, Hooman (2015).
739:10.1126/science.1135491
693:: 24–31. Archived from
687:"The Tiles of Infinity"
648:10.1126/science.1135491
493:Wooden screen from the
4203:Institute For Figuring
4115:The 'Life' of a Carpet
3940:A Treatise on Painting
2976:Indo-Saracenic Revival
1922:Indo-Saracenic Revival
1322:(multicoloured ashlar)
413:
396:
388:
380:
372:
51:
39:
27:
4084:George David Birkhoff
4058:Ernest Hanbury Hankin
3926:De divina proportione
3906:Piero della Francesca
3885:Leon Battista Alberti
3472:Piero della Francesca
3111:Hyperboloid structure
2931:Empire of the Sultans
1659:Congregational mosque
1117:(four-arch structure)
411:
394:
386:
378:
370:
132:angle specifications
45:
33:
22:
4310:Architecture in Iran
4290:Islamic architecture
4009:Frederik Macody Lund
3880:Filippo Brunelleschi
3761:Hamid Naderi Yeganeh
3623:La condition humaine
2894:Arab World Institute
2704:Ottoman illumination
1983:Ottoman architecture
1973:Moorish architecture
1968:Islamic architecture
1963:Iranian architecture
1386:Sebka (Darj-wa-ktaf)
1240:(or müezzin mahfili)
900:Islamic architecture
768:Supplemental figures
521:Moorish architecture
184:(non-convex hexagon)
82:Islamic architecture
4234:Mathematical beauty
4159:Rhythm of Structure
4102:Gödel, Escher, Bach
3898:De re aedificatoria
3529:The Ancient of Days
3148:Projective geometry
3077:Mathematics and art
2020: •
2007: •
1993:Yemeni architecture
1978:Mughal architecture
1958:Berber architecture
1953:Arabic architecture
1617:Salsabil (fountain)
1351:Islamic calligraphy
731:2007Sci...315.1106L
725:(5815): 1106–1110.
640:2007Sci...315.1106L
634:(5815): 1106–1110.
253:rotational symmetry
113:
4239:Patterns in nature
4096:Douglas Hofstadter
3722:Desmond Paul Henry
3712:Bathsheba Grossman
3644:The Swallow's Tail
3565:Giorgio de Chirico
3437:Sydney Opera House
3292:Croatian interlace
2971:Aniconism in Islam
2909:Toronto (Aga Khan)
2866:Khalili Collection
2731:Geometric patterns
2139:Bahmani and Deccan
1694:Kuttab (or maktab)
691:Saudi Aramco World
422:Different patterns
414:
397:
389:
381:
373:
318:Paul J. Steinhardt
111:
62:are a set of five
52:
40:
28:
4272:
4271:
4125:
4124:
4089:Aesthetic Measure
3960:Sebastiano Serlio
3934:Leonardo da Vinci
3824:
3823:
3816:Margaret Wertheim
3477:Leonardo da Vinci
3043:
3042:
2712:
2711:
2567:
2566:
2539:Hardstone carving
2436:Chinese influence
2287:
2286:
2273:Stucco decoration
2037:
2036:
1884:
1883:
1640:
1639:
1627:Shading Umbrellas
1411:Stucco decoration
1311:For overview, see
1126:Four-centred arch
245:
244:
126:number of corners
50:pattern on right.
4322:
4260:
4259:
4110:Nikos Salingaros
3833:
3801:Hiroshi Sugimoto
3751:Robert Longhurst
3697:Helaman Ferguson
3652:Crockett Johnson
3581:Circle Limit III
3550:Danseuse au café
3457:
3427:Pyramid of Khufu
3190:
3070:
3063:
3056:
3047:
2882:Majorelle Garden
2578:
2411:Hispano-Moresque
2305:
2295:
2104:Anatolian Seljuk
2084:
2064:
2057:
2050:
2041:
2030:Islam portal
2028:
2027:
2026:
2015:
2014:
1649:
1314:Islamic ornament
1193:South Asian dome
1121:Discharging arch
1102:
1075:
919:Anatolian Seljuk
893:
886:
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865:
863:
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682:
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623:
617:
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598:
592:
591:
563:
516:Aperiodic tiling
490:
470:
450:
430:
330:tilings such as
328:quasicrystalline
303:
302:
114:
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4325:
4324:
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4321:
4320:
4319:
4275:
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4273:
4268:
4248:
4244:Sacred geometry
4217:
4183:Ars Mathematica
4171:
4121:
4032:
3985:
3972:Andrea Palladio
3868:
3861:De architectura
3820:
3776:Antoine Pevsner
3756:Jeanette McLeod
3707:Susan Goldstine
3656:
3515:
3509:
3446:
3432:Sagrada Família
3393:
3335:
3203:Algorithmic art
3191:
3182:
3178:Wallpaper group
3116:Minimal surface
3079:
3074:
3044:
3039:
3008:Moorish Revival
2956:
2950:
2918:
2835:Calligraphy Art
2801:
2794:
2756:
2708:
2682:
2609:
2573:
2563:
2529:Enamelled glass
2502:
2481:
2440:
2392:
2347:
2308:Regional styles
2296:
2283:
2209:
2180:Sudano-Sahelian
2087:Regional styles
2073:
2068:
2038:
2033:
2024:
2022:
2009:
1997:
1941:
1932:Moorish Revival
1910:
1880:
1846:Albarrana tower
1834:
1763:
1750:in modern Iran)
1664:Dar al-Muwaqqit
1636:
1587:(fountain type)
1572:
1566:
1529:
1523:
1514:Reflecting pool
1509:Persian gardens
1504:Paradise garden
1472:
1449:(entrance hall)
1420:
1376:Nagash painting
1298:
1220:
1214:
1165:
1136:Lambrequin arch
1103:
1094:
1066:
1037:Sudano-Sahelian
902:
897:
860:
858:
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845:
843:
838:
830:
825:
824:
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550:
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511:
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482:
471:
462:
451:
442:
431:
419:
402:
361:
332:Penrose tilings
310:
283:
277:
261:
102:
96:built in 1453.
17:
12:
11:
5:
4328:
4326:
4318:
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4055:
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4034:
4033:
4031:
4030:
4029:
4028:
4026:The Greek Vase
4018:
4017:
4016:
4006:
4005:
4004:
3993:
3991:
3987:
3986:
3984:
3983:
3982:
3981:
3969:
3968:
3967:
3957:
3956:
3955:
3948:Albrecht Dürer
3945:
3944:
3943:
3931:
3930:
3929:
3917:
3916:
3915:
3903:
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3901:
3894:
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3851:
3850:
3839:
3837:
3830:
3826:
3825:
3822:
3821:
3819:
3818:
3813:
3811:Roman Verostko
3808:
3803:
3798:
3793:
3788:
3786:Alba Rojo Cama
3783:
3778:
3773:
3768:
3763:
3758:
3753:
3748:
3743:
3742:
3741:
3732:Charles Jencks
3729:
3724:
3719:
3717:George W. Hart
3714:
3709:
3704:
3699:
3694:
3689:
3684:
3679:
3670:
3664:
3662:
3658:
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3628:
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3613:
3612:
3605:
3598:
3591:
3584:
3572:
3567:
3562:
3561:
3560:
3553:
3544:Jean Metzinger
3541:
3540:
3539:
3532:
3519:
3517:
3511:
3510:
3508:
3507:
3506:
3505:
3493:
3491:Albrecht Dürer
3488:
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3474:
3469:
3463:
3461:
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3252:
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3237:
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3225:
3220:
3210:
3208:Anamorphic art
3205:
3199:
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3192:
3185:
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3180:
3175:
3170:
3165:
3164:
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3158:
3150:
3145:
3140:
3139:
3138:
3136:Camera obscura
3133:
3123:
3118:
3113:
3108:
3103:
3098:
3093:
3087:
3085:
3081:
3080:
3075:
3073:
3072:
3065:
3058:
3050:
3041:
3040:
3038:
3037:
3035:Topkapı Scroll
3032:
3025:
3020:
3015:
3010:
3005:
3000:
2999:
2998:
2993:
2983:
2978:
2973:
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2924:
2920:
2919:
2917:
2916:
2911:
2906:
2901:
2890:
2885:
2874:
2869:
2858:British Museum
2854:
2849:
2842:Islamic Museum
2838:
2827:
2822:
2817:
2812:
2806:
2804:
2796:
2795:
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2792:
2787:
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2592:
2586:
2584:
2575:
2569:
2568:
2565:
2564:
2562:
2561:
2560:
2559:
2553:Stained glass
2551:
2546:
2541:
2536:
2531:
2526:
2524:Damascus steel
2521:
2516:
2510:
2508:
2504:
2503:
2501:
2500:
2495:
2489:
2487:
2483:
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2474:
2469:
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2075:
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2067:
2066:
2059:
2052:
2044:
2035:
2034:
2002:
1999:
1998:
1996:
1995:
1990:
1985:
1980:
1975:
1970:
1965:
1960:
1955:
1949:
1947:
1946:Category pages
1943:
1942:
1940:
1939:
1934:
1929:
1924:
1918:
1916:
1912:
1911:
1909:
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1903:
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1858:
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1836:
1835:
1833:
1832:
1827:
1822:
1820:Medina quarter
1817:
1812:
1807:
1802:
1797:
1792:
1787:
1782:
1777:
1771:
1769:
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1629:
1624:
1619:
1614:
1608:
1606:Riwaq (arcade)
1603:
1598:
1593:
1588:
1582:
1576:
1574:
1568:
1567:
1565:
1564:
1559:
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1539:
1533:
1531:
1525:
1524:
1522:
1521:
1516:
1511:
1506:
1501:
1496:
1494:Islamic garden
1491:
1486:
1480:
1478:
1474:
1473:
1471:
1470:
1465:
1460:
1455:
1450:
1444:
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1216:
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1206:
1201:
1196:
1173:
1171:
1167:
1166:
1164:
1163:
1158:
1153:
1148:
1143:
1141:Multifoil arch
1138:
1133:
1131:Horseshoe arch
1128:
1123:
1118:
1111:
1109:
1105:
1104:
1097:
1095:
1093:
1092:
1087:
1081:
1079:
1072:
1068:
1067:
1065:
1064:
1059:
1054:
1049:
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1034:
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1024:
1023:
1022:
1017:
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1002:
992:
987:
982:
973:
972:
971:
966:
961:
956:
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936:
931:
926:
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910:
908:
904:
903:
898:
896:
895:
888:
881:
873:
867:
866:
851:
836:
829:
828:External links
826:
823:
822:
789:
771:
760:
707:
677:
618:
612:978-3848003808
611:
593:
552:
551:
549:
546:
544:
543:
538:
536:Topkapı Scroll
533:
528:
526:Penrose tiling
523:
518:
512:
510:
507:
502:
501:
492:
485:
483:
472:
465:
463:
455:Topkapı Palace
452:
445:
443:
432:
425:
423:
418:
415:
401:
398:
360:
357:
344:Topkapi Palace
340:Topkapi Scroll
309:
306:
279:Main article:
276:
273:
260:
257:
243:
242:
239:
236:
233:
228:
221:
220:
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15:
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10:
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6:
4:
3:
2:
4327:
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4308:
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4288:
4286:
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4282:
4280:
4265:
4264:
4255:
4254:
4251:
4245:
4242:
4240:
4237:
4235:
4232:
4230:
4229:Droste effect
4227:
4226:
4224:
4220:
4214:
4211:
4209:
4208:Mathemalchemy
4206:
4204:
4201:
4199:
4196:
4194:
4191:
4189:
4186:
4184:
4181:
4180:
4178:
4176:Organizations
4174:
4168:
4167:
4163:
4161:
4160:
4156:
4154:
4153:
4149:
4147:
4146:
4145:Lumen Naturae
4142:
4140:
4139:
4135:
4134:
4132:
4128:
4116:
4113:
4112:
4111:
4108:
4104:
4103:
4099:
4098:
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4090:
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4035:
4027:
4024:
4023:
4022:
4019:
4015:
4012:
4011:
4010:
4007:
4003:
4000:
3999:
3998:
3997:Samuel Colman
3995:
3994:
3992:
3988:
3980:
3979:
3975:
3974:
3973:
3970:
3966:
3963:
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3840:
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3834:
3831:
3827:
3817:
3814:
3812:
3809:
3807:
3806:Daina Taimiņa
3804:
3802:
3799:
3797:
3794:
3792:
3791:Reza Sarhangi
3789:
3787:
3784:
3782:
3779:
3777:
3774:
3772:
3769:
3767:
3764:
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3728:
3725:
3723:
3720:
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3715:
3713:
3710:
3708:
3705:
3703:
3702:Peter Forakis
3700:
3698:
3695:
3693:
3690:
3688:
3685:
3683:
3680:
3678:
3674:
3671:
3669:
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3663:
3659:
3653:
3650:
3646:
3645:
3641:
3639:
3638:
3634:
3633:
3632:
3631:Salvador Dalí
3629:
3625:
3624:
3620:
3619:
3618:
3617:René Magritte
3615:
3611:
3610:
3606:
3604:
3603:
3599:
3597:
3596:
3592:
3590:
3589:
3588:Print Gallery
3585:
3583:
3582:
3578:
3577:
3576:
3573:
3571:
3568:
3566:
3563:
3559:
3558:
3557:L'Oiseau bleu
3554:
3552:
3551:
3547:
3546:
3545:
3542:
3538:
3537:
3533:
3531:
3530:
3526:
3525:
3524:
3523:William Blake
3521:
3520:
3518:
3512:
3504:
3503:
3499:
3498:
3497:
3494:
3492:
3489:
3485:
3484:
3483:Vitruvian Man
3480:
3479:
3478:
3475:
3473:
3470:
3468:
3467:Paolo Uccello
3465:
3464:
3462:
3458:
3455:
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3415:
3413:
3410:
3408:
3405:
3404:
3402:
3400:
3396:
3390:
3389:
3388:Pi in the Sky
3385:
3383:
3382:
3378:
3376:
3375:
3371:
3369:
3368:
3364:
3362:
3361:
3360:Mathemalchemy
3357:
3355:
3354:
3350:
3348:
3345:
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3338:
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3329:
3327:
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3236:
3233:
3229:
3228:Vastu shastra
3226:
3224:
3221:
3219:
3218:Geodesic dome
3216:
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3209:
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3149:
3146:
3144:
3143:Plastic ratio
3141:
3137:
3134:
3132:
3131:Camera lucida
3129:
3128:
3127:
3124:
3122:
3119:
3117:
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2544:Ivory carving
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2019:
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1805:Hasht-Bihisht
1803:
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1679:Jama'at Khana
1677:
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1499:Mughal garden
1497:
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708:
697:on 2010-01-13
696:
692:
688:
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589:
585:
581:
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574:(2). p. 350.
573:
569:
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560:
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554:
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444:
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435:Tomb of Hafez
429:
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119:
116:
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112:Caption text
109:
107:
99:
97:
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91:
87:
83:
79:
78:
73:
69:
65:
61:
58:
57:
49:
44:
37:
32:
25:
21:
4295:Tessellation
4261:
4164:
4157:
4150:
4143:
4136:
4130:Publications
4114:
4100:
4088:
4074:
4062:
4048:
4025:
4021:Jay Hambidge
4014:Ad Quadratum
4013:
4001:
3976:
3964:
3952:
3938:
3924:
3920:Luca Pacioli
3910:
3896:
3889:
3859:
3847:
3771:Hinke Osinga
3766:István Orosz
3736:
3727:Anthony Hill
3682:Scott Draves
3677:Erik Demaine
3661:Contemporary
3642:
3635:
3621:
3607:
3600:
3593:
3586:
3579:
3575:M. C. Escher
3555:
3548:
3534:
3527:
3500:
3496:Parmigianino
3481:
3412:Hagia Sophia
3386:
3379:
3372:
3365:
3358:
3351:
3235:Computer art
3213:Architecture
3173:Tessellation
3156:Architecture
3106:Golden ratio
3027:
3023:Pseudo-Kufic
2963:
2943:
2936:
2929:
2852:Kuala Lumpur
2750:
2739:
2277:
2129:Indo-Islamic
2119:Great Seljuk
2079:Architecture
2021:
2008:
2005:Islamic arts
1785:Caravanserai
1345:
1310:
1264:Loudspeakers
1189:Persian dome
1151:Pointed arch
949:Indo-Islamic
939:Great Seljuk
859:. Retrieved
844:. Retrieved
806:
802:
792:
783:
763:
722:
716:
710:
699:. Retrieved
695:the original
690:
680:
631:
627:
621:
602:
596:
571:
568:Nexus Netw J
567:
503:
498:caravanserai
475:Green Mosque
403:
362:
349:
336:
322:self-similar
311:
284:
269:tessellation
262:
246:
230:
208:
187:
165:
143:
108:names, are:
103:
75:
59:
55:
54:
53:
47:
35:
23:
4315:Iranian art
4300:Islamic art
4070:G. H. Hardy
3873:Renaissance
3843:Polykleitos
3781:Tony Robbin
3692:John Ernest
3687:Jan Dibbets
3637:Crucifixion
3460:Renaissance
3314:Mathematics
3287:Celtic knot
3250:Fractal art
3152:Proportion
3126:Perspective
2955:Principles,
2923:Exhibitions
2876:Marrakech (
2872:Los Angeles
2840:Jerusalem (
2802:collections
2753:Calligraphy
2633:Indo-Muslim
2615:Calligraphy
2549:Mosque lamp
2507:Other media
2426:Mina'i ware
2315:Bangladeshi
2071:Islamic art
1632:Windcatcher
1613:(courtyard)
1366:Mosque lamp
1346:Girih tiles
1303:Decorations
1181:Arabic dome
314:Peter J. Lu
288:are lines (
265:tile mosaic
86:Darb-i Imam
4279:Categories
4044:Owen Jones
3891:De pictura
3796:Oliver Sin
3746:Andy Lomas
3595:Relativity
3326:String art
3240:Fiber arts
3121:Paraboloid
3029:Stilfragen
2957:influences
2829:Istanbul (
2762:The garden
2718:Decoration
2687:Other arts
2582:Miniatures
2467:Embroidery
2421:Lustreware
2280:Decoration
2243:Mashrabiya
2151:Indonesian
1915:Influences
1830:Well house
1601:Mashrabiya
1249:Hussainiya
1185:Onion dome
976:Indonesian
964:Qutb Shahi
861:2007-03-14
846:2007-03-14
809:: 75–108.
701:2010-01-08
548:References
188:Sormeh Dan
166:Shesh Band
100:Five tiles
88:shrine in
34:Patterned
3855:Vitruvius
3829:Theorists
3609:Waterfall
3514:19th–20th
3442:Taj Mahal
3422:Parthenon
3399:Buildings
3353:Continuum
3321:Sculpture
3297:Interlace
3091:Algorithm
2991:Grotesque
2904:Singapore
2888:Melbourne
2726:Arabesque
2155:Malaysian
1889:Resources
1652:Religious
1622:Shabestan
1580:Hypostyle
1562:Shadirvan
1331:Arabesque
1254:Imamzadeh
1219:Religious
1199:Semi-dome
1146:Ogee arch
1115:Chahartaq
1078:Materials
1005:Almoravid
980:Malaysian
588:253596464
290:strapwork
72:strapwork
4263:Category
3990:Romantic
3668:Max Bill
3602:Reptiles
3417:Pantheon
3374:Octacube
3340:Artworks
3282:Knotting
3270:Muqarnas
3168:Symmetry
3096:Catenary
3084:Concepts
2996:Moresque
2856:London (
2800:Museums,
2785:Paradise
2770:Charbagh
2751:See also
2653:Nastaliq
2643:Muhaqqaq
2574:the book
2486:Woodwork
2445:Textiles
2406:Fritware
2278:See also
2263:Muqarnas
2258:Mocárabe
2215:Elements
2003:Part of
1839:Military
1775:Baradari
1768:Civilian
1591:Jharokha
1552:Mechouar
1489:Charbagh
1432:Andaruni
1406:Socarrat
1371:Muqarnas
1269:Maqsurah
1161:Vaulting
1090:Tadelakt
1071:Elements
1020:Zayyanid
1000:Aghlabid
755:10374218
747:17322056
672:10374218
664:17322056
656:20039057
531:Tadelakt
509:See also
495:Nishapur
459:Istanbul
417:Examples
226:pentagon
224:regular
137:regular
4222:Related
3836:Ancient
3570:Man Ray
3516:Century
3452:Artists
3309:Origami
3223:Pyramid
3101:Fractal
3013:Mudéjar
2914:Tripoli
2892:Paris (
2862:V&A
2790:Persian
2780:Ottoman
2694:Muraqqa
2673:Thuluth
2658:Persian
2605:Persian
2600:Ottoman
2572:Arts of
2557:Shabaka
2431:Persian
2398:Pottery
2383:Turkish
2378:Persian
2353:Carpets
2342:Ottoman
2338:Turkish
2332:Safavid
2320:Persian
2253:Minaret
2228:Banna'i
2200:Umayyad
2195:Timurid
2185:Swahili
2175:Ottoman
2170:Moorish
2160:Iranian
2134:Bengali
2114:Fatimid
2109:Chinese
2099:Ayyubid
2094:Abbasid
1937:Mudéjar
1901:ArchNet
1851:Alcázar
1724:Musalla
1709:Maqbara
1699:Madrasa
1689:Külliye
1684:Khanqah
1674:Gongbei
1573:cooling
1571:Passive
1537:Chhatri
1530:objects
1528:Outdoor
1477:Gardens
1453:Mirador
1391:Shabaka
1381:Qashani
1336:Banna'i
1279:Minaret
1221:objects
1211:(eaves)
1209:Chhajja
1156:Squinch
1057:Umayyad
1052:Timurid
1042:Swahili
1027:Ottoman
1010:Almohad
995:Moorish
985:Iranian
954:Bengali
934:Fatimid
929:Chinese
924:Ayyubid
914:Abbasid
727:Bibcode
718:Science
636:Bibcode
628:Science
325:fractal
294:Persian
249:radians
209:Torange
204:rhombus
182:bow tie
161:hexagon
139:decagon
121:Persian
106:Persian
90:Isfahan
4037:Modern
3673:Martin
3536:Newton
3331:Tiling
3275:Zellij
3245:4D art
2898:Louvre
2878:Museum
2825:Ghazni
2810:Berlin
2775:Mughal
2746:Zellij
2678:Tughra
2628:Diwani
2623:Arabic
2595:Mughal
2590:Arabic
2498:Minbar
2493:Khatam
2477:Suzani
2472:Soumak
2457:Damask
2388:Prayer
2371:Motifs
2268:Sitara
2248:Mihrab
2205:Yemeni
2165:Mamluk
2144:Mughal
1861:Kasbah
1810:Kasbah
1800:Hammam
1795:Ghorfa
1780:Bazaar
1759:Zawiya
1748:takyeh
1719:Mosque
1669:Dargah
1596:Kucheh
1542:Eidgah
1468:Zenana
1416:Zellij
1401:Sitara
1396:Shamsa
1284:Minbar
1274:Mihrab
1259:Kiswah
1244:Gonbad
1108:Arches
1062:Yemeni
1032:Somali
1015:Hafsid
990:Mamluk
969:Mughal
959:Deccan
907:Styles
753:
745:
670:
662:
654:
609:
586:
541:Zellij
441:, 1935
439:Shiraz
352:Gothic
129:convex
70:using
4305:Girih
3848:Canon
3304:Music
3260:Girih
3196:Forms
3161:Human
2815:Cairo
2740:tiles
2736:Girih
2699:Hilya
2668:Taliq
2648:Naskh
2638:Kufic
2534:Glass
2519:Brass
2514:Music
2452:Batik
2416:Iznik
2366:Kilim
2328:Qajar
2324:Early
2223:Ablaq
2190:Tatar
2124:Hausa
1876:Ribat
1871:Qalat
1856:Amsar
1815:Mahal
1754:Türbe
1744:Takya
1739:Surau
1734:Rauza
1729:Qubba
1714:Mazar
1704:Maqam
1645:Types
1557:Sebil
1447:Liwan
1437:Harem
1425:Rooms
1341:Girih
1326:Alfiz
1320:Ablaq
1294:Zarih
1289:Qibla
1238:Dikka
1233:Bedug
1228:Anaza
1204:Tajug
1170:Roofs
1085:Qadad
1047:Tatar
944:Hausa
751:S2CID
668:S2CID
652:JSTOR
584:S2CID
479:Bursa
296:word
286:Girih
281:Girih
275:Girih
241:108°
231:Pange
154:144°
77:girih
64:tiles
60:tiles
56:Girih
48:girih
38:tiles
36:Girih
26:tiles
24:Girih
3675:and
3265:Jali
2831:Arts
2820:Doha
2663:Sini
2462:Ikat
2301:Arts
2238:Jali
2233:Iwan
1866:Ksar
1825:Souq
1746:(or
1611:Sahn
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