tiling theory

Tiling theory studies how shapes can cover a surface completely without overlaps or gaps using repeated patterns. It explores which shapes, arrangements, or patterns can fill spaces efficiently and uniformly, such as in mosaics or tessellations. The theory helps understand the mathematical principles behind creating seamless designs and has applications in art, architecture, and material science. In essence, it examines the possibilities and limitations of covering surfaces with various geometric forms, revealing both aesthetic and structural insights into pattern formation.