1 00:00:00,000 --> 00:00:09,910 In Islamic culture, geometry is everywhere. 2 00:00:10,589 --> 00:00:15,289 You can find it in mosques, madrasas, palaces, and private homes. 3 00:00:16,070 --> 00:00:18,949 This tradition began in the 8th century CE, 4 00:00:19,449 --> 00:00:21,510 during the early history of Islam, 5 00:00:21,510 --> 00:00:26,350 when craftsmen took pre-existing motifs from Roman and Persian cultures 6 00:00:26,350 --> 00:00:30,010 and developed them into new forms of visual expression. 7 00:00:30,010 --> 00:00:34,689 This period of history was a golden age of Islamic culture, 8 00:00:35,009 --> 00:00:37,649 during which many achievements of previous civilizations 9 00:00:37,649 --> 00:00:40,270 were preserved and further developed, 10 00:00:40,710 --> 00:00:45,130 resulting in fundamental advancements in scientific study and mathematics. 11 00:00:46,409 --> 00:00:50,189 Accompanying this was an increasingly sophisticated use of abstraction 12 00:00:50,189 --> 00:00:53,390 and complex geometry in Islamic art, 13 00:00:53,390 --> 00:00:57,429 from intricate floral motifs adorning carpets and textiles 14 00:00:57,429 --> 00:01:01,229 to patterns of tile work that seemed to repeat infinitely, 15 00:01:01,789 --> 00:01:05,010 inspiring wonder and contemplation of eternal order. 16 00:01:06,150 --> 00:01:08,769 Despite the remarkable complexity of these designs, 17 00:01:09,090 --> 00:01:11,870 they can be created with just a compass to draw circles 18 00:01:11,870 --> 00:01:14,230 and a ruler to make lines within them. 19 00:01:14,769 --> 00:01:19,890 And from these simple tools emerges a kaleidoscopic multiplicity of patterns. 20 00:01:20,769 --> 00:01:21,849 So how does that work? 21 00:01:22,329 --> 00:01:24,489 Well, everything starts with a circle. 22 00:01:25,090 --> 00:01:28,189 The first major decision is, how will you divide it up? 23 00:01:28,769 --> 00:01:33,390 Most patterns split the circle into four, five, or six equal sections, 24 00:01:33,569 --> 00:01:36,930 and each division gives rise to distinctive patterns. 25 00:01:37,849 --> 00:01:44,150 There's an easy way to determine whether any pattern is based on four-fold, five-fold, or six-fold symmetry. 26 00:01:44,750 --> 00:01:47,730 Most contain stars surrounded by petal shapes. 27 00:01:48,530 --> 00:01:52,849 Counting the number of rays on a starburst, or the number of petals around it, 28 00:01:52,849 --> 00:01:56,290 tells us what category the pattern falls into. 29 00:01:56,290 --> 00:02:00,129 A star with six rays, or surrounded by six petals, 30 00:02:00,129 --> 00:02:03,129 belongs in the six-fold category. 31 00:02:03,129 --> 00:02:08,069 One with eight petals is part of the four-fold category, and so on. 32 00:02:08,069 --> 00:02:12,969 There's another secret ingredient in these designs, an underlying grid. 33 00:02:12,969 --> 00:02:15,770 Invisible but essential to every pattern, 34 00:02:15,770 --> 00:02:20,770 the grid helps determine the scale of the composition before work begins, 35 00:02:20,770 --> 00:02:22,530 keeps the pattern accurate, 36 00:02:22,530 --> 00:02:27,050 and facilitates the invention of incredible new patterns. 37 00:02:27,050 --> 00:02:30,409 Let's look at an example of how these elements come together. 38 00:02:30,409 --> 00:02:32,889 We'll start with a circle within a square 39 00:02:32,889 --> 00:02:35,610 and divide it into eight equal parts. 40 00:02:35,610 --> 00:02:38,789 We can then draw a pair of crisscrossing lines 41 00:02:38,789 --> 00:02:41,550 and overlay them with another two. 42 00:02:41,550 --> 00:02:44,090 These lines are called construction lines, 43 00:02:44,090 --> 00:02:46,530 and by choosing a set of their segments, 44 00:02:46,530 --> 00:02:50,370 we'll form the basis of our repeating pattern. 45 00:02:50,370 --> 00:02:54,349 Many different designs are possible from the same construction lines 46 00:02:54,349 --> 00:02:56,930 just by picking different segments. 47 00:02:56,930 --> 00:02:59,310 And the full pattern finally emerges 48 00:02:59,310 --> 00:03:03,969 when we create a grid with many repetitions of this one tile 49 00:03:03,969 --> 00:03:06,909 in a process called tessellation. 50 00:03:06,909 --> 00:03:09,590 By choosing a different set of construction lines, 51 00:03:09,590 --> 00:03:12,370 we might have created this pattern, 52 00:03:12,370 --> 00:03:13,750 or this one. 53 00:03:13,750 --> 00:03:16,870 The possibilities are virtually endless. 54 00:03:16,870 --> 00:03:20,870 We can follow the same steps to create six-fold patterns. 55 00:03:20,870 --> 00:03:24,870 By drawing construction lines over a circle divided into six parts 56 00:03:24,870 --> 00:03:28,870 and then tessellating it, we can make something like this. 57 00:03:28,870 --> 00:03:32,870 Here's another six-fold pattern that has appeared across the centuries 58 00:03:32,870 --> 00:03:34,870 and all over the Islamic world, 59 00:03:34,870 --> 00:03:40,870 including Marrakech, Agra, Konya, and the Alhambra. 60 00:03:40,870 --> 00:03:44,870 Four-fold patterns fit in a square grid, 61 00:03:44,870 --> 00:03:49,270 and six-fold patterns in a hexagonal grid. 62 00:03:49,270 --> 00:03:53,270 Five-fold patterns, however, are more challenging to tessellate 63 00:03:53,270 --> 00:03:57,270 because pentagons don't neatly fill a surface. 64 00:03:57,270 --> 00:04:00,469 So instead of just creating a pattern in a pentagon, 65 00:04:00,469 --> 00:04:04,069 other shapes have to be added to make something that is repeatable, 66 00:04:04,069 --> 00:04:08,270 resulting in patterns that may seem confoundingly complex 67 00:04:08,270 --> 00:04:12,069 but are still relatively simple to create. 68 00:04:12,069 --> 00:04:16,410 Also, tessellation is not constrained to simple geometric shapes, 69 00:04:16,750 --> 00:04:18,889 as M.C. Escher's work demonstrates. 70 00:04:19,509 --> 00:04:22,029 And while the Islamic geometric design tradition 71 00:04:22,029 --> 00:04:25,250 doesn't tend to employ elements like fish and faces, 72 00:04:25,250 --> 00:04:30,550 it does sometimes make use of multiple shapes to craft complex patterns. 73 00:04:31,810 --> 00:04:35,990 This more than 1,000-year-old tradition has wielded basic geometry 74 00:04:35,990 --> 00:04:40,949 to produce works that are intricate, decorative, and pleasing to the eye. 75 00:04:40,949 --> 00:04:44,089 and these craftsmen prove just how much is possible 76 00:04:44,089 --> 00:04:48,009 with some artistic intuition, creativity, dedication, 77 00:04:48,649 --> 00:04:50,310 and a great compass and ruler.