Mathematical tiling refers to the arrangement of shapes, called tiles, to cover a surface without any gaps or overlaps. These tiles can be regular shapes, like squares and triangles, or irregular shapes. Tiling is often studied in geometry and can be used in various fields, including art, architecture, and computer graphics. One famous example of mathematical tiling is the work of M.C. Escher, who created intricate patterns that demonstrate how shapes can fit together in visually appealing ways. Tiling can also involve concepts like symmetry and periodicity, which help in understanding how different patterns can repeat across a surface.