0:00:06.804,0:00:10.722 In Islamic culture, [br]geometry is everywhere. 0:00:10.722,0:00:16.294 You can find it in mosques,[br]madrasas, palaces and private homes. 0:00:16.294,0:00:22.141 This tradition began in the 8th century CE[br]during the early history of Islam, 0:00:22.141,0:00:26.710 when craftsman took preexisting motifs[br]from Roman and Persian cultures 0:00:26.710,0:00:31.208 and developed them into new forms[br]of visual expression. 0:00:31.208,0:00:35.159 This period of history was a golden age[br]of Islamic culture, 0:00:35.159,0:00:38.044 during which many achievements [br]of previous civilizations 0:00:38.044,0:00:40.740 were preserved and further developed, 0:00:40.740,0:00:46.522 resulting in fundamental advancements[br]in scientific study and mathematics. 0:00:46.522,0:00:50.860 Accompanying this was an increasingly[br]sophisticated use of abstraction 0:00:50.860,0:00:53.979 and complex geometry in Islamic art, 0:00:53.979,0:00:57.740 from intricate floral motifs[br]adorning carpets and textiles, 0:00:57.740,0:01:01.887 to patterns of tilework that seemed[br]to repeat infinitely, 0:01:01.887,0:01:06.340 inspiring wonder [br]and contemplation of eternal order. 0:01:06.340,0:01:09.135 Despite the remarkable complexity[br]of these designs, 0:01:09.135,0:01:12.380 they can be created [br]with just a compass to draw circles 0:01:12.380,0:01:14.953 and a ruler to make lines within them, 0:01:14.953,0:01:20.936 and from these simple tools emerges [br]a kaleidoscope multiplicity of patterns. 0:01:20.936,0:01:22.746 So how does that work? 0:01:22.746,0:01:25.370 Well, everything starts with a circle. 0:01:25.370,0:01:28.946 The first major decision [br]is how will you divide it up? 0:01:28.946,0:01:34.222 Most patterns split the circle[br]into four, five or six equal sections. 0:01:34.222,0:01:37.964 And each division gives rise[br]to distinctive patterns. 0:01:37.964,0:01:41.810 There's an easy way to determine[br]whether any pattern is based on fourfold, 0:01:41.810,0:01:43.129 fivefold, 0:01:43.129,0:01:45.001 or sixfold symmetry. 0:01:45.001,0:01:48.215 Most contain stars surrounded[br]by petal shapes. 0:01:48.215,0:01:51.074 Counting the number [br]of rays on a starburst, 0:01:51.074,0:01:53.117 or the number of petals around it, 0:01:53.117,0:01:56.626 tells us what category [br]the pattern falls into. 0:01:56.626,0:02:00.315 A star with six rays,[br]or surrounded by six petals, 0:02:00.315,0:02:03.468 belongs in the sixfold category. 0:02:03.468,0:02:08.531 One with eight petals is part[br]of the fourfold category, and so on. 0:02:08.531,0:02:11.228 There's another secret ingredient[br]in these designs: 0:02:11.228,0:02:13.418 an underlying grid. 0:02:13.418,0:02:16.044 Invisible, but essential to every pattern, 0:02:16.044,0:02:21.190 the grid helps determine the scale[br]of the composition before work begins, 0:02:21.190,0:02:22.569 keeps the pattern accurate, 0:02:22.569,0:02:26.700 and facilitates the invention [br]of incredible new patterns. 0:02:26.700,0:02:30.813 Let's look at an example of how these[br]elements come together. 0:02:30.813,0:02:35.983 We'll start with a circle within a square,[br]and divide it into eight equal parts. 0:02:35.983,0:02:39.161 We can then draw a pair[br]of criss-crossing lines 0:02:39.161,0:02:41.895 and overlay them with another two. 0:02:41.895,0:02:44.528 These lines are called construction lines, 0:02:44.528,0:02:46.902 and by choosing a set of their segments, 0:02:46.902,0:02:50.711 we'll form the basis [br]of our repeating pattern. 0:02:50.711,0:02:54.508 Many different designs are possible[br]from the same construction lines 0:02:54.508,0:02:57.307 just by picking different segments. 0:02:57.307,0:02:59.457 And the full pattern finally emerges 0:02:59.457,0:03:04.428 when we create a grid with many[br]repetitions of this one tile 0:03:04.428,0:03:07.330 in a process called tessellation. 0:03:07.330,0:03:09.856 By choosing a different set [br]of construction lines, 0:03:09.856,0:03:12.752 we might have created this pattern, 0:03:12.752,0:03:14.225 or this one. 0:03:14.225,0:03:17.243 The possibilities are virtually endless. 0:03:17.243,0:03:21.037 We can follow the same steps[br]to create sixfold patterns 0:03:21.037,0:03:25.083 by drawing construction lines[br]over a circle divided into six parts, 0:03:25.083,0:03:29.931 and then tessellating it,[br]we can make something like this. 0:03:29.931,0:03:33.458 Here's another sixfold pattern[br]that has appeared across the centuries 0:03:33.458,0:03:35.531 and all over the Islamic world, 0:03:35.531,0:03:41.239 including Marrakesh, Agra, Konya[br]and the Alhambra. 0:03:41.239,0:03:49.437 Fourfold patterns fit in a square grid,[br]and sixfold patterns in a hexagonal grid. 0:03:49.437,0:03:53.282 Fivefold patterns, however,[br]are more challenging to tessellate 0:03:53.282,0:03:57.487 because pentagons [br]don't neatly fill a surface, 0:03:57.487,0:04:00.421 so instead of just creating [br]a pattern in a pentagon, 0:04:00.421,0:04:04.084 other shapes have to be added[br]to make something that is repeatable, 0:04:04.084,0:04:08.129 resulting in patterns that may seem[br]confoundingly complex, 0:04:08.129,0:04:11.881 but are still relatively simple to create. 0:04:11.881,0:04:16.886 Also, tessellation is not constrained[br]to simple geometric shapes, 0:04:16.886,0:04:19.681 as M.C. Escher's work demonstrates. 0:04:19.681,0:04:22.189 And while the Islamic [br]geometric design tradition 0:04:22.189,0:04:25.782 doesn't tend to employ elements [br]like fish and faces, 0:04:25.782,0:04:31.912 it does sometimes make use of multiple [br]shapes to craft complex patterns. 0:04:31.912,0:04:36.260 This more than 1,000-year-old tradition[br]has wielded basic geometry 0:04:36.260,0:04:41.489 to produce works that are intricate,[br]decorative and pleasing to the eye. 0:04:41.489,0:04:44.317 And these craftsman prove just how[br]much is possible 0:04:44.317,0:04:51.030 with some artistic intuition, creativity,[br]dedication and a great compass and ruler.