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  • In Islamic culture, geometry is everywhere.

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

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

  • when craftsman took preexisting motifs from Roman and Persian cultures

  • and developed them into new forms of visual expression.

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

  • during which many achievements of previous civilizations

  • were preserved and further developed,

  • resulting in fundamental advancements in scientific study and mathematics.

  • Accompanying this was an increasingly sophisticated use

  • of abstraction and complex geometry in Islamic art,

  • from intricate floral motifs adorning carpets and textiles,

  • to patterns of tile work that seemed to repeat infinitely,

  • inspiring wonder and contemplation of eternal order.

  • Despite the remarkable complexity of these designs,

  • they can be created with just a compass to draw circles and a ruler to make lines within them,

  • and from these simple tools emerges a kaleidoscope multiplicity of patterns.

  • So how does that work?

  • Well, everything starts with a circle.

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

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

  • And each division gives rise to distinctive patterns.

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

  • fivefold,

  • or sixfold symmetry.

  • Most contain stars surrounded by petal shapes.

  • Counting the number of rays on a starburst,

  • or the number of petals around it,

  • tells us what category the pattern falls into.

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

  • belongs in the sixfold category.

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

  • There's another secret ingredient in these designs:

  • an underlying grid.

  • Invisible, but essential to every pattern,

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

  • keeps the pattern accurate,

  • and facilitates the invention of incredible new patterns.

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

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

  • We can then draw a pair of criss-crossing lines

  • and overlay them with another two.

  • These lines are called construction lines,

  • and by choosing a set of their segments,

  • we'll form the basis of our repeating pattern.

  • Many different designs are possible from the same construction lines just by picking different segments.

  • And the full pattern finally emerges

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

  • in a process called tessellation.

  • By choosing a different set of construction lines,

  • we might have created this pattern,

  • or this one.

  • The possibilities are virtually endless.

  • We can follow the same steps to create sixfold patterns

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

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

  • Here's another sixfold pattern that has appeared across the centuries and all over the Islamic world,

  • including Marrakesh, Agra, Konya and the Alhambra.

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

  • Fivefold patterns, however, are more challenging to tessellate

  • because pentagons don't neatly fill a surface,

  • so instead of just creating a pattern in a pentagon,

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

  • resulting in patterns that may seem confoundingly complex,

  • but are still relatively simple to create.

  • Also, tessellation is not constrained to simple geometric shapes,as M.C. Escher's work demonstrates.

  • And while the Islamic geometric design tradition doesn't tend to employ elements like fish and faces,

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

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

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

  • And these craftsman prove just how much is possible with some artistic intuition, creativity, dedication and a great compass and ruler.

In Islamic culture, geometry is everywhere.

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B2 TED-Ed pattern islamic grid geometry construction

【TED-Ed】The complex geometry of Islamic design - Eric Broug

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    稲葉白兎 posted on 2015/05/22
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