Opening Ceremony, UNESCO Paris, 21 January 2014

Peter Lu, Postdoctoral Research Fellow, Harvard University, USA

Modern math in medieval Islamic architecture

Peter Lu
Postdoctoral Research Fellow, Harvard University, USA


The conventional view holds that girih (geometric starand-polygon) patterns in medieval Islamic architecture were conceived by their designers as a network of zigzagging lines and drafted directly with a straightedge and a compass.

I will describe recent findings that, by 1200 CE, a conceptual breakthrough occurred in which girih patterns were reconceived as tessellations of a special set of equilateral polygons (girih tiles) decorated with lines. These girih tiles enabled the creation of increasingly complex periodic girih patterns.

By the 15th century, the tessellation approach was combined with self-similar transformations to construct nearly-perfect quasicrystalline patterns. Quasicrystal patterns have remarkable properties: they do not repeat periodically, have special symmetry and were not understood in the West until the 1970s. I will discuss some of the properties of Islamic quasicrystalline tilings and their relation to the Penrose tiling, perhaps the best-known quasicrystal pattern.


The lecture given by Peter Lu at UNESCO in January 2014 was an abridged version of an hour-long presentation he made in December 2007 during a colloquium organized by the Physics Department of Harvard University. Dr Lu asks that a link be made to his longer presentation on the same topic.

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