page_title: Alhambra
section_title: In mathematics
hierarchical_section_title: Alhambra / Influence / In mathematics
caption_attribution_description: Tessellation in the Alhambra. This was one of the tilings sketched by M. C. Escher in 1936.
context_page_description: The Alhambra is a palace and fortress complex located in Granada, Andalusia, Spain. It was originally constructed as a small fortress in AD 889 on the remains of Roman fortifications, and then largely ignored until its ruins were renovated and rebuilt in the mid-13th century by the Nasrid emir Mohammed ben Al-Ahmar of the Emirate of Granada, who built its current palace and walls with many beautiful, intricate details. It was converted into a royal palace in 1333 by Yusuf I, Sultan of Granada. After the conclusion of the Christian Reconquista in 1492, the site became the Royal Court of Ferdinand and Isabella, and the palaces were partially altered in the Renaissance style. In 1526 Charles I & V commissioned a new Renaissance palace better befitting the Holy Roman Emperor in the revolutionary Mannerist style influenced by humanist philosophy in direct juxtaposition with the Nasrid Andalusian architecture, but it was ultimately never completed due to Morisco rebellions in Granada.
  Alhambra's last flowering of Islamic palaces was built for the final Muslim emirs in Spain during the decline of the Nasrid dynasty, who were increasingly subject to the Christian Kings of Castile.
context_section_description: The Alhambra tiles are remarkable in that they contain nearly all, if not all, of the seventeen mathematically possible wallpaper groups. This is a unique accomplishment in world architecture. M. C. Escher's visit in 1922 and study of the Moorish use of symmetries in the Alhambra tiles inspired his subsequent work on tessellation, which he called "regular divisions of the plane".
caption: Tessellations like this inspired M.C. Escher's work.
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