Islamic Geometry

Geometry is a very important element in Islamic art. We can find all kinds of geometric figures in mosaics made by Muslims, in architecture and in ornaments.

Where more geometric figures are found is in the tiling. The tiles are formed by small pieces of ceramics with different colors and shapes that together forms geometric shapes of great complexity. In the Alhambra there is a great variety of mosaics that advance in complexity over time. In the Nasrid art exist thus simple compositions, based on the repetition of one or two figures; and complex compositions, in which different motives move and rotate to generate  new geometric forms at a higher level.




The geometrical frameworks of the decoration of Hispano-Muslim art are based on three key elements to tessellate the plane, that is to cover a surface using polygons without leaving gaps. Specific:

1. A polygonal motif as the basis of the compositions.

2. The creation of compositions through isometries, that is to say, movements of the plane of said motives conserving their proportions. This is carried out by:

Translation: moving to a new fixed position without changing the orientation.
Rotation: direct rotation of the motif on a fixed point.
Symmetry: reflection or inverse mirror image of the motif.

Slipped symmetry: translation of the reflection on the same axis without a fixed point.

3. The linear growth of such compositions that could be continued to infinity.


These tessellations can be done through polygonal motifs, simpler to make those that abound in the tiling of the Alhambra; or of non-polygonal motifs. These second ones imply a greater mastery because it supposes a more laborious process of creation to obtain non-polygonal forms that fit together. As an example of non-polygonal shapes, the most popular is the trisquel or "bow-tie" shape, created through the transformation of an equilateral triangle.