Taj-Al-Mulk Northward Dome (with v-fold motif), Jameh mosque, Isfahan, built1088 (photo: R. Henry), alongside item showing the path of Venus from James Ferguson's, Astronomy Explained Upon Sir Isaac Newton's Principles, 1799 ed., plate III, opp. p. 67.

Geometry  – The Language of Symmetry in Islamic Art

past Richard Henry

Throughout the ages mystics & theologians accept used geometry equally a contemplative focus, as it enables the viewer a vision of the underyling club of both the creation and the natural world . The cyclical movement of heavenly bodies, which Plato described as the 'music of the spheres', finds its Earthly reflection in the natural symmetries establish throughout nature and about strikingly within the earth of flowers, the proportions of which are governed by unproblematic geometric laws. The origin of the word 'creation' is beautification (from which we derive the mod word 'cosmetics') and the adornment of sacred buildings with both floral and geometric patterns makes the viewer sensitive to the subtle harmonies uniting the natural globe around us with the cosmos.

In Islamic art the geometric figure of the circle represents the primordial symbol of unity and the ultimate source of all diversity in creation. The natural division of the circle into regular divisions is the ritual starting point for many traditional Islamic patterns, as demonstrated in the drawings beneath.

The  pattern above (15 th century) from Yazd in Iran is derived from half dozen regular divisions of the circumvolve. From this a regular filigree of triangles is established, on height of which the design is elaborated. Note how the complex tracery of pattern interweaves with the basic design which appears in white outline in the photograph above.

A family of geometric tiles (above), derived from the octagram (khatam – 8 pointed star) class a 'jigsaw' puzzle, which through unlike combinations can generate a myriad of stunning designs. These are typical of the ceramic cut tile pieces used in mosaics thoughout Kingdom of morocco, where they are known every bit 'zillij' and  Andalucia, where they are known every bit 'alicatado', from the early medieval period onwards. These shapes are still cut by hand in modern day Morocco.

In the Alhambra (14th C), Spain (above), geometric design is perfectly integrated with biomorphic design (arabesque) and calligraphy.  These are the three distinct, only complementary, disciplines that contain Islamic art. They form a iii-fold hierarchy in which geometry is seen as foundational. This is ofttimes signified by its use on the floors or lower parts of walls, as shown in the image higher up.

The decorative elements deployed apply a range of symmetries that have at present been classified as belonging to distinct mathematical groups, only the subtlety and beauty of the designs is unparallelled in mod mathematical thinking.

Islamic designers used the total range of Archimedean tilings (comprised of simple polygons) first discovered by the Greeks, simply added to and expanded upon these with extraordinary visual and spatial ingenuity. The pattern higher up (afterwards Paul Marchant) is based on elements of medieval designs typically constitute in Cairo. Find the pattern of underlying polygons: hexagons, triangles, squares, dodecagons. The underling tiling pattern is commonly subconscious beneath the terminal design, every bit if backside a veil, but the viewer is always given an intimation of the subconscious lodge and this is role of what gives the designs their meditative power.

With a compass and ruler an Iranian master craftsman demonstrates a method for setting out a pattern which employs 10-fold radial symmetry. Note the construction of the decagram (10-pointed star). This is the key generative motif for Western farsi 'girih' patterns.

The four examples above prove how to derive a range of classic motifs from the decagram (there are several more). These form the ground of 12th century Iranian 'girih' patterns, which take been linked to Roger Penrose'south famous not-periodic tilings, i.east. patterns that can extend to infinity without regular repetition.

The pattern below is a cutting tile mosaic pattern from the inside tomb of Persian poet Hafez in Shiraz, Iran. Note how the family unit of geometric 'girih' motifs derived from the decagram is variously deployed with great ingenuity across a curved surface in the blueprint beneath.

Shiraz – Aramgah-e Hafez. Tomb of Hafez, tombstone placed past Karim Khan 1773. Octagonal pavillion added 1935 (photo: R. Henry).