[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:06.80,0:00:10.72,Default,,0000,0000,0000,,In Islamic culture, \Ngeometry is everywhere.
Dialogue: 0,0:00:10.72,0:00:16.29,Default,,0000,0000,0000,,You can find it in mosques,\Nmadrasas, palaces and private homes.
Dialogue: 0,0:00:16.29,0:00:22.14,Default,,0000,0000,0000,,This tradition began in the 8th century CE\Nduring the early history of Islam,
Dialogue: 0,0:00:22.14,0:00:26.71,Default,,0000,0000,0000,,when craftsmen took preexisting motifs\Nfrom Roman and Persian cultures
Dialogue: 0,0:00:26.71,0:00:31.21,Default,,0000,0000,0000,,and developed them into new forms\Nof visual expression.
Dialogue: 0,0:00:31.21,0:00:35.16,Default,,0000,0000,0000,,This period of history was a golden age\Nof Islamic culture,
Dialogue: 0,0:00:35.16,0:00:38.04,Default,,0000,0000,0000,,during which many achievements \Nof previous civilizations
Dialogue: 0,0:00:38.04,0:00:40.74,Default,,0000,0000,0000,,were preserved and further developed,
Dialogue: 0,0:00:40.74,0:00:46.52,Default,,0000,0000,0000,,resulting in fundamental advancements\Nin scientific study and mathematics.
Dialogue: 0,0:00:46.52,0:00:50.86,Default,,0000,0000,0000,,Accompanying this was an increasingly\Nsophisticated use of abstraction
Dialogue: 0,0:00:50.86,0:00:53.98,Default,,0000,0000,0000,,and complex geometry in Islamic art,
Dialogue: 0,0:00:53.98,0:00:57.74,Default,,0000,0000,0000,,from intricate floral motifs\Nadorning carpets and textiles,
Dialogue: 0,0:00:57.74,0:01:01.89,Default,,0000,0000,0000,,to patterns of tilework that seemed\Nto repeat infinitely,
Dialogue: 0,0:01:01.89,0:01:06.34,Default,,0000,0000,0000,,inspiring wonder \Nand contemplation of eternal order.
Dialogue: 0,0:01:06.34,0:01:09.14,Default,,0000,0000,0000,,Despite the remarkable complexity\Nof these designs,
Dialogue: 0,0:01:09.14,0:01:12.38,Default,,0000,0000,0000,,they can be created \Nwith just a compass to draw circles
Dialogue: 0,0:01:12.38,0:01:14.95,Default,,0000,0000,0000,,and a ruler to make lines within them.
Dialogue: 0,0:01:14.95,0:01:20.94,Default,,0000,0000,0000,,And from these simple tools emerges \Na kaleidoscope multiplicity of patterns.
Dialogue: 0,0:01:20.94,0:01:22.75,Default,,0000,0000,0000,,So how does that work?
Dialogue: 0,0:01:22.75,0:01:25.37,Default,,0000,0000,0000,,Well, everything starts with a circle.
Dialogue: 0,0:01:25.37,0:01:28.95,Default,,0000,0000,0000,,The first major decision \Nis how will you divide it up?
Dialogue: 0,0:01:28.95,0:01:34.22,Default,,0000,0000,0000,,Most patterns split the circle\Ninto four, five or six equal sections.
Dialogue: 0,0:01:34.22,0:01:37.96,Default,,0000,0000,0000,,And each division gives rise\Nto distinctive patterns.
Dialogue: 0,0:01:37.96,0:01:41.81,Default,,0000,0000,0000,,There's an easy way to determine\Nwhether any pattern is based on fourfold,
Dialogue: 0,0:01:41.81,0:01:43.13,Default,,0000,0000,0000,,fivefold,
Dialogue: 0,0:01:43.13,0:01:45.00,Default,,0000,0000,0000,,or sixfold symmetry.
Dialogue: 0,0:01:45.00,0:01:48.22,Default,,0000,0000,0000,,Most contain stars surrounded\Nby petal shapes.
Dialogue: 0,0:01:48.22,0:01:51.07,Default,,0000,0000,0000,,Counting the number \Nof rays on a starburst,
Dialogue: 0,0:01:51.07,0:01:53.12,Default,,0000,0000,0000,,or the number of petals around it,
Dialogue: 0,0:01:53.12,0:01:56.63,Default,,0000,0000,0000,,tells us what category \Nthe pattern falls into.
Dialogue: 0,0:01:56.63,0:02:00.32,Default,,0000,0000,0000,,A star with six rays,\Nor surrounded by six petals,
Dialogue: 0,0:02:00.32,0:02:03.47,Default,,0000,0000,0000,,belongs in the sixfold category.
Dialogue: 0,0:02:03.47,0:02:08.53,Default,,0000,0000,0000,,One with eight petals is part\Nof the fourfold category, and so on.
Dialogue: 0,0:02:08.53,0:02:11.23,Default,,0000,0000,0000,,There's another secret ingredient\Nin these designs:
Dialogue: 0,0:02:11.23,0:02:13.42,Default,,0000,0000,0000,,an underlying grid.
Dialogue: 0,0:02:13.42,0:02:16.04,Default,,0000,0000,0000,,Invisible, but essential to every pattern,
Dialogue: 0,0:02:16.04,0:02:21.19,Default,,0000,0000,0000,,the grid helps determine the scale\Nof the composition before work begins,
Dialogue: 0,0:02:21.19,0:02:22.57,Default,,0000,0000,0000,,keeps the pattern accurate,
Dialogue: 0,0:02:22.57,0:02:26.70,Default,,0000,0000,0000,,and facilitates the invention \Nof incredible new patterns.
Dialogue: 0,0:02:26.70,0:02:30.81,Default,,0000,0000,0000,,Let's look at an example of how these\Nelements come together.
Dialogue: 0,0:02:30.81,0:02:35.98,Default,,0000,0000,0000,,We'll start with a circle within a square,\Nand divide it into eight equal parts.
Dialogue: 0,0:02:35.98,0:02:39.16,Default,,0000,0000,0000,,We can then draw a pair\Nof criss-crossing lines
Dialogue: 0,0:02:39.16,0:02:41.90,Default,,0000,0000,0000,,and overlay them with another two.
Dialogue: 0,0:02:41.90,0:02:44.53,Default,,0000,0000,0000,,These lines are called construction lines,
Dialogue: 0,0:02:44.53,0:02:46.90,Default,,0000,0000,0000,,and by choosing a set of their segments,
Dialogue: 0,0:02:46.90,0:02:50.71,Default,,0000,0000,0000,,we'll form the basis \Nof our repeating pattern.
Dialogue: 0,0:02:50.71,0:02:54.51,Default,,0000,0000,0000,,Many different designs are possible\Nfrom the same construction lines
Dialogue: 0,0:02:54.51,0:02:57.31,Default,,0000,0000,0000,,just by picking different segments.
Dialogue: 0,0:02:57.31,0:02:59.46,Default,,0000,0000,0000,,And the full pattern finally emerges
Dialogue: 0,0:02:59.46,0:03:04.43,Default,,0000,0000,0000,,when we create a grid with many\Nrepetitions of this one tile
Dialogue: 0,0:03:04.43,0:03:07.33,Default,,0000,0000,0000,,in a process called tessellation.
Dialogue: 0,0:03:07.33,0:03:09.86,Default,,0000,0000,0000,,By choosing a different set \Nof construction lines,
Dialogue: 0,0:03:09.86,0:03:12.75,Default,,0000,0000,0000,,we might have created this pattern,
Dialogue: 0,0:03:12.75,0:03:14.22,Default,,0000,0000,0000,,or this one.
Dialogue: 0,0:03:14.22,0:03:17.24,Default,,0000,0000,0000,,The possibilities are virtually endless.
Dialogue: 0,0:03:17.24,0:03:21.04,Default,,0000,0000,0000,,We can follow the same steps\Nto create sixfold patterns
Dialogue: 0,0:03:21.04,0:03:25.08,Default,,0000,0000,0000,,by drawing construction lines\Nover a circle divided into six parts,
Dialogue: 0,0:03:25.08,0:03:29.93,Default,,0000,0000,0000,,and then tessellating it,\Nwe can make something like this.
Dialogue: 0,0:03:29.93,0:03:33.46,Default,,0000,0000,0000,,Here's another sixfold pattern\Nthat has appeared across the centuries
Dialogue: 0,0:03:33.46,0:03:35.53,Default,,0000,0000,0000,,and all over the Islamic world,
Dialogue: 0,0:03:35.53,0:03:41.24,Default,,0000,0000,0000,,including Marrakesh, Agra, Konya\Nand the Alhambra.
Dialogue: 0,0:03:41.24,0:03:49.44,Default,,0000,0000,0000,,Fourfold patterns fit in a square grid,\Nand sixfold patterns in a hexagonal grid.
Dialogue: 0,0:03:49.44,0:03:53.28,Default,,0000,0000,0000,,Fivefold patterns, however,\Nare more challenging to tessellate
Dialogue: 0,0:03:53.28,0:03:57.49,Default,,0000,0000,0000,,because pentagons \Ndon't neatly fill a surface,
Dialogue: 0,0:03:57.49,0:04:00.42,Default,,0000,0000,0000,,so instead of just creating \Na pattern in a pentagon,
Dialogue: 0,0:04:00.42,0:04:04.08,Default,,0000,0000,0000,,other shapes have to be added\Nto make something that is repeatable,
Dialogue: 0,0:04:04.08,0:04:08.13,Default,,0000,0000,0000,,resulting in patterns that may seem\Nconfoundingly complex,
Dialogue: 0,0:04:08.13,0:04:11.88,Default,,0000,0000,0000,,but are still relatively simple to create.
Dialogue: 0,0:04:11.88,0:04:16.89,Default,,0000,0000,0000,,Also, tessellation is not constrained\Nto simple geometric shapes,
Dialogue: 0,0:04:16.89,0:04:19.68,Default,,0000,0000,0000,,as M.C. Escher's work demonstrates.
Dialogue: 0,0:04:19.68,0:04:22.19,Default,,0000,0000,0000,,And while the Islamic \Ngeometric design tradition
Dialogue: 0,0:04:22.19,0:04:25.78,Default,,0000,0000,0000,,doesn't tend to employ elements \Nlike fish and faces,
Dialogue: 0,0:04:25.78,0:04:31.91,Default,,0000,0000,0000,,it does sometimes make use of multiple \Nshapes to craft complex patterns.
Dialogue: 0,0:04:31.91,0:04:36.26,Default,,0000,0000,0000,,This more than 1,000-year-old tradition\Nhas wielded basic geometry
Dialogue: 0,0:04:36.26,0:04:41.49,Default,,0000,0000,0000,,to produce works that are intricate,\Ndecorative and pleasing to the eye.
Dialogue: 0,0:04:41.49,0:04:44.32,Default,,0000,0000,0000,,And these craftsmen prove just how\Nmuch is possible
Dialogue: 0,0:04:44.32,0:04:51.03,Default,,0000,0000,0000,,with some artistic intuition, creativity,\Ndedication and a great compass and ruler.