Kitchen Floors and the Alhambra Palace

M. C. Escher, Victor Vasarely and Bridget Riley are artists who have explored tessellations – continuous and potentially infinite patterns of shapes, often seen in mosaic designs or tiled floors. Mathematicians since Archimedes have devoted themselves to trying to figure out what kinds of polygons can be used to “tile the plane.” Students learn about this process from the point of view of both mathematician and artist, exploring what kinds of shapes lend themselves to “tiling,” and creating their own tessellated artwork. 

Mathematical Concepts

  • Polygons
  • Geometric vs. organic shapes
  • Angle measurement: interior and exterior angles  
  • Symmetry
  • Area
  • Translation, rotation, reflection, glide reflection


Court of the lions - websiteEarly Islamic art avoided religious symbols, possibly in deliberate contrast to Christian art of the same (Medieval) era. Instead, its design elements were based on geometric shapes, using organic forms that were highly stylized in decorative tracery that covers an entire surface with beautiful and sometimes complex patterns. The relationship of one shape to another was more important than the complete pattern, which was seen as decoration. The repeated shapes are similar to a repeated melodic or rhythmic pattern in music.