Historical references on the construction of Islamic geometric patterns are rare, but what we do have offers fascinating glimpses of practical methods, thought processes, and the world-view of medieval Islamic craftsmen.

A Book on Those Geometric Constructions Which Are Necessary for a Craftsman, written by the tenth century mathematician and astronomer Abū al-Wafā’ Būzjānī (940-998) and an anonymous Persian compendium entitled On Similar and Complementary Interlocking Figures, a practical manual on geometry, appended to a Persian translation of al-Būzjānī’s text.

We will work through a series of constructions from these documents. Evolving from theoretical principles of Euclidean geometry, some of the diagrams can be traced to architectural scrolls and ornamental architectural solutions. These exercises will provide us with some understanding of the early roots of the incredibly complex vocabulary of the Islamic geometric patterns and their relationship to such disciplines as surveying and arithmetic.

We will explore how questions of practical/applied geometry were discussed by mathematicians and practitioners of various crafts, and how the practice of drawing geometric designs constituted  a tradition of recoding and transmitting architectural knowledge. The diagrams in these documents visually evoke concepts of beauty and order rooted in the harmony of proportionally interrelated figures and, in part, explain the timeless fascination that geometry holds for contemporary artists and practitioners.

Fī tadākhul al-ashkāl al-mutashābiha aw al-mutawāfiqa (On Similar and Complementary Interlocking Figures) or the Anonymous Compendium, appended to the Persian translation of al-Būzjānī’s text in the Paris codex. MS Persan 169,