Mathematics and arts: Connections between theory and practice in the medieval Islamic world
The author gives a detailed description (and, in the appendix, a preliminary Arabic text) of a geometric text (whose compilation he attributes to a student of the 10th Cent. mathematician Abu'l Wafā al Būzjānī) which reports his discussions with artisans (probably makers of mosaics) about the construction of a large square from smaller squares (or the inverse problem) by cutting and pasting. The resulting figures as bases for tilings give very pleasing results and occasionally use nontrivial mathematics, also in the disproof of some constructions used by artisans. A second part deals with a later Persian manuscript, of which a complete edition and translation is promised, and which deals not only with squares but also with pentagons and decagons and the related star polygons. He concludes that the artisans engaged in creating the outstanding tilings of Islamic art never acquired the geometric knowledge required for their craft but continued to pick the brains of professional mathematicians.
scientific article; zbMATH DE number 1496592