Geometric Figures in the Facades of the Khoja Akhmet Yasawi Mausoleum

The purpose of the current study was to comprehensively investigate the facades of the Mausoleum of Khoja Akhmet Yasawi, its geometric patterns and the mathematical laws used for their design. To do this, the writings of medieval mathematicians were analysed, and their principles considered to model the geometric patterns of the facades. The paper describes the evolution of geometric laws in the Islamic world from the 7th to the 9th century. The Mausoleum of Khoja Akhmet Yasawi is one of the best examples of geometric architectural applications from the 14th-15th century. The facades of Khoja Akhmet Yasawi seemingly rely on the methods of two mathematicians, Al-Farabi and Al-Khwarizmi. To a greater extent, the ornaments derive from dividing equilateral triangles, parallelograms and polygons to create geometric figures. The façade patterns of the Khoja Akhmet Yasawi complex require careful calculation and preparation due to their conciseness and harmony, giving insight into the fields of arithmetic, geometry and architecture and architects’ education during the 14th-15th century.