In general, as indicated above, there is little evidence of interaction between ‘theoretical’ mathematicians and artisan geometricists in Medieval Islam – however, there are a small number of surviving texts that have been cited as evidence that there were at least some exceptions to this rule…
Gulru Necipoglu1 and Alpay Özdural2 single out a couple of examples - one originating in the 10th/4th century involving the mathematician and astrologer Abu al-Wafa al-Buzjani, and a later, anonymous Persian text from the 14th/8th century on ‘Interlocking Figures’.
Al-Wafa al-Buzjani (940-998 CE/329-380 AH) was the author of a manual of practical geometry Risâla fimâ yahtâju al-sâni’u min a’mâl al-handasa (‘On the Geometric Constructions Necessary for the Artisan’), of which four known hand-written versions survive - one in Arabic and three in Persian. The original work was written in Baghdad, in Arabic, but no longer exists, and each of the later copies has some missing information and chapters. The surviving Arabic version (which is kept in the library of Ayasofya, Istanbul) although not original, is more complete than the others. The best known of the three Persian manuscripts is kept in the National Library in Paris, France. Although clearly directed at artist/craftsmen, the general tone of this work is of a somewhat petulant criticism of their reluctance to adopt ‘proper’ (i.e. Euclidean) methods of geometrical construction.
The Fî tadâkhul al-ashkâl al-mutashâbiha aw al-mutawâfiqa (‘On interlocking similar or congruent figures’) is a geometric manual by an unknown author, probably originating in Tabriz during the Ilkhanid period. There seems to be as much interest here in the ‘puzzle’ aspect of the figures involved as in their use in decorative ornament, indicating that it may not have been directed exclusively at artist/craftsmen.
There are a few other, even less specific, allusions to the involvement of mathematicians with decorative ornamental schemes. The polymath/inventor Al-Jazari drew and described an elaborate plan for a door in his book on ‘Ingenious Mechanical Devises’ (fig. 24), although George Saliba has pointed out that the translation on which this is based may be faulty3. And there is a tantalising reference by Omar Khayyam (no less) to ‘meetings of artisans and geometers’4, but this allusion too is vague and open to misinterpretation.
In summary, it is difficult, on the basis of available evidence, to make any substantial claims for the notion of academic involvement in the genre of Islamic geometric ornamentation.