WEBVTT

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In Islamic culture, 
geometry is everywhere.

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You can find it in mosques,
madrasas, palaces and private homes.

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This tradition began in the 8th century CE
during the early history of Islam,

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when craftsmen took preexisting motifs
from Roman and Persian cultures

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and developed them into new forms
of visual expression.

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This period of history was a golden age
of Islamic culture,

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during which many achievements 
of previous civilizations

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were preserved and further developed,

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resulting in fundamental advancements
in scientific study and mathematics.

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Accompanying this was an increasingly
sophisticated use of abstraction

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and complex geometry in Islamic art,

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from intricate floral motifs
adorning carpets and textiles,

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to patterns of tilework that seemed
to repeat infinitely,

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inspiring wonder 
and contemplation of eternal order.

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Despite the remarkable complexity
of these designs,

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they can be created 
with just a compass to draw circles

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and a ruler to make lines within them.

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And from these simple tools emerges 
a kaleidoscope multiplicity of patterns.

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So how does that work?

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Well, everything starts with a circle.

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The first major decision 
is how will you divide it up?

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Most patterns split the circle
into four, five or six equal sections.

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And each division gives rise
to distinctive patterns.

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There's an easy way to determine
whether any pattern is based on fourfold,

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fivefold,

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or sixfold symmetry.

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Most contain stars surrounded
by petal shapes.

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Counting the number 
of rays on a starburst,

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or the number of petals around it,

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tells us what category 
the pattern falls into.

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A star with six rays,
or surrounded by six petals,

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belongs in the sixfold category.

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One with eight petals is part
of the fourfold category, and so on.

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There's another secret ingredient
in these designs:

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an underlying grid.

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Invisible, but essential to every pattern,

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the grid helps determine the scale
of the composition before work begins,

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keeps the pattern accurate,

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and facilitates the invention 
of incredible new patterns.

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Let's look at an example of how these
elements come together.

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We'll start with a circle within a square,
and divide it into eight equal parts.

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We can then draw a pair
of criss-crossing lines

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and overlay them with another two.

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These lines are called construction lines,

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and by choosing a set of their segments,

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we'll form the basis 
of our repeating pattern.

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Many different designs are possible
from the same construction lines

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just by picking different segments.

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And the full pattern finally emerges

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when we create a grid with many
repetitions of this one tile

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in a process called tessellation.

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By choosing a different set 
of construction lines,

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we might have created this pattern,

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or this one.

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The possibilities are virtually endless.

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We can follow the same steps
to create sixfold patterns

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by drawing construction lines
over a circle divided into six parts,

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and then tessellating it,
we can make something like this.

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Here's another sixfold pattern
that has appeared across the centuries

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and all over the Islamic world,

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including Marrakesh, Agra, Konya
and the Alhambra.

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Fourfold patterns fit in a square grid,
and sixfold patterns in a hexagonal grid.

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Fivefold patterns, however,
are more challenging to tessellate

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because pentagons 
don't neatly fill a surface,

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so instead of just creating 
a pattern in a pentagon,

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other shapes have to be added
to make something that is repeatable,

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resulting in patterns that may seem
confoundingly complex,

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but are still relatively simple to create.

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Also, tessellation is not constrained
to simple geometric shapes,

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as M.C. Escher's work demonstrates.

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And while the Islamic 
geometric design tradition

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doesn't tend to employ elements 
like fish and faces,

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it does sometimes make use of multiple 
shapes to craft complex patterns.

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This more than 1,000-year-old tradition
has wielded basic geometry

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to produce works that are intricate,
decorative and pleasing to the eye.

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And these craftsmen prove just how
much is possible

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with some artistic intuition, creativity,
dedication and a great compass and ruler.