Medieval Islamic Tiling Reveals Mathematical Savvy

Medieval Islamic designers used elaborate geometrical tiling patterns at least 500 years before Western mathematicians developed the concept.

The geometric design, called "girih", was widely used to decorate Islamic buildings but the advanced mathematical concept within the patterns was not recognised, until now. Physicist Peter Lu at Harvard University in Cambridge, Massachusetts, US, realised the 15^th-century tiles formed so-called Penrose geometric patterns, when he spotted them on a visit to Uzbekistan.

Scholars had thought the girih were created by drawing a zigzag network of lines with a straight edge and compass. But when Lu looked at them, he recognised the regular but non-repetitive patterns of Penrose tiling - a concept developed in the West only in the 1970s.

Simple periodic patterns can be generated easily by repeating a unit cell of several elements, a technique widely used in tile patterns, but the rotational symmetry possible is limited. In the 1970s, Roger Penrose at the University of Oxford in the UK showed, for the first time, that "thick" and "thin" rhombus-shaped tiles could cover a plane, creating a non-repetitive pattern with five-fold rotational symmetry.