The Dividing of the Sphere in Domes of Medieval Anatolia

The stylistic language of art and architecture in medieval Anatolia largely consists of geometric features with various levels of mathematical complexity. Whereas the two-dimensional graphic designs employ certain geometric relations and rules, their making, in three-dimensional space, relies on the spatial material qualities and the overall architectural form more than just visual transformations. For understanding how their architectonic harmony was implemented, it is crucial to consider not only the geometric design but also other parameters such as the surface geometry, the physical properties of the material, and the crafting technique. Under the patronage of Seljuks in Anatolia, the rigorous application of the decoration program on historical buildings manifests a collaboration coordinated by a master builder between mathematicians, designers, and craftsmen. Geometric patterns were applied to all kinds of building surfaces. Dome decorations particularly addressed challenges of building with spherical geometry. We investigate the historical ways to construct continuous patterns on dome surfaces and how each simultaneously handles aspects of geometrical calculation, the design, and construction processes.