April 09, 2008

The art of geometry

The repeating geometric patterns found in Islamic art fascinate the eye and captivate the mind. They don't so much inspire the imagination as draw it on towards a contemplation of the infinite.

The repeating patterns in Islamic design are based on the exploration of geometric principles - most importantly, the relation between circles and hexagons, and certain happy ratios.

Eva Wilson explains (cobbled together from her book Islamic Designs):-
The circumference of a circle can be divide into six equal parts by its radius to form a hexagon. When alternative points of the figure are joined by straight lines two triangles are produced which together make up a six-pointed star.

The ratio between the diameters of hexagons based on concentric six-pointed stars drawn from the hexagon's corners is 1:2. When the concentric stars are drawn from the hexagon's mid points, the ratio between the heights of the hexagons is also 1:2.

The hexagon, together with its associated six-pointed star, is the most important geometric construction in Islamic art. It is a common basis for repeat patterns and many designs of apparently different character are drawn on hexagon-based grids.

A hexagon-based pattern is also used in circular designs. A circle surrounded by six other circles of the same size forms a hexagon. Allowing the peripheral circles to encroach on the inner circle produces a variety of geometric and decorative characteristics.

Tassellatura from the Alhambra, Granada