There is so much to look at and admire in Alhambra Palace (Granada, Spain) – exquisite rooms decorated with stone and wood carvings, finest ornaments and calligraphy; night sky represented in ceilings built of thousands of pieces of wood; gardens, courtyards and fountains; monuments, towers, archways – the list is endless. Quite possibly, an immense wealth of ornamental patterns, friezes, mosaics, star designs, and brickwork motifs tops the list. Among those, mosaics are – mathematically – the most interesting and the most intriguing.

Scientists and artists working in the Islamic world pushed geometry to its limits, creating patterns and configurations whose sophistication has not been surpassed. Investigating numerous possibilities, based on experience and long tradition, architects and builders of the Alhambra (14th century) created all possible mosaics – in the sense of the mathematical classification of plane crystallographic groups. Mathematics behind all this is intuitive: we will discuss the concept of symmetry and see how it can be used to analyze mosaics.