Number, geometry, and aesthetics in the Islamic mathematical tradition: on the origins of quasicrystal patterns

In the last fifty years, a significant literature has emerged in the fields of architecture, mathematics, materials science and art history on the determination of the mathematical structures of geometric ornaments and their production stages. The existing literature investigates how the quasicrystal ornaments encountered after the 13th century were produced by the artists of the period using only compasses and rulers. This article examines the emergence of quasicrystal ornaments in the context of the history and philosophy of mathematics and contributes to the literature in this respect. In Islamic civilization, from the 9th century onwards, mathematics experienced a radical transformation with the redefinition of the concept of number. This process influenced not only arithmetic and algebra, but also the understanding of geometry and the aesthetic principles used in works of art. This study aims to reveal that the geometric patterns observed in Turkish-Islamic architecture, including motifs that bear visual similarities to structures discussed in quasicrystal research, are not only aesthetic elements but also conscious reflections of the mathematical knowledge of the period in art.