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WonderGeometric design fact

Girih tiles are a set of five shapes that medieval Islamic craftsmen used to plan the interlaced star-and-line patterns on walls and domes. Some of their 15th-century patterns come close to a kind of order mathematicians only described in the 1970s.

Lu and Steinhardt, Science, 2007

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The story behind the card

Girih is Persian for 'knot'. Each of the five tiles, a decagon, a pentagon, an elongated hexagon, a bowtie and a rhombus, carries decorative lines. Laid edge to edge, the lines join into continuous bands, so a maker could build a vast design from a few pieces. In 2007 the physicists Peter Lu and Paul Steinhardt showed that some patterns, notably on the Darb-i Imam shrine in Isfahan (1453), come close to quasicrystalline order: an arrangement that is highly regular yet never repeats itself exactly, like the Penrose tilings that mathematicians described in the 1970s. The craftsmen reached it through geometry and practice, centuries before anyone had the mathematics to describe it.

Türkçe oku
Girih karoları, Orta Çağ İslam ustalarının duvarlara ve kubbelere işlenen iç içe geçmiş yıldızlı desenleri planlarken kullandığı beş biçimlik bir takımdır. 15. yüzyıldan kalma bazı desenler, matematikçilerin ancak 1970'lerde tanımladığı bir düzene çok yaklaşır.
Lu ve Steinhardt, Science dergisi, 2007

Girih, Farsçada “düğüm” demektir. Beş karonun her biri (ongen, beşgen, uzun altıgen, papyon ve eşkenar dörtgen) üzerinde süsleme çizgileri taşır. Karolar kenar kenara dizildiğinde bu çizgiler birleşip kesintisiz şeritlere dönüşür; böylece bir usta birkaç parçayla dev bir desen kurabilirdi. Fizikçiler Peter Lu ve Paul Steinhardt 2007'de, başta İsfahan'daki Darb-ı İmam türbesi (1453) olmak üzere bazı desenlerin kuazikristal düzene çok yaklaştığını gösterdi. Kuazikristal düzen, son derece düzenli olduğu hâlde kendini hiçbir zaman aynen tekrarlamayan bir diziliştir; matematikçilerin 1970'lerde tanımladığı Penrose döşemeleri buna örnektir. Ustalar bu düzene, onu anlatacak matematikten yüzyıllar önce geometri bilgisi ve deneyimle ulaşmıştı.

Sources and further reading

Background reading: Girih tiles
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