9.2 Isometric Geometry in Islamic Perceptual Culture
Whereas the isometric polyhedral geometry today associated with Islamic
cultures developed in approximately the tenth century, earlier Islamic arts
and architecture employed the golden ratio, valorized since antiquity. A
proportion frequent in nature and based on the irrational number (phi),
1.6180339..., the golden ratio was extolled as epitomizing harmonious
beauty from Pythagoras to Plato and constructed mathematically in
Euclid’sElements. It embodies a pre-arithmetical geometry practiced by
Roman craftsmen and discussed by thefirst-century BCE architect and
engineer Vitruvius.^21 This understanding of beauty reentered Christian
Europe with the twelfth-century reintroduction of Greek philosophy and
science from Arabic translations. It underlies ideal human and architec-
tural proportions established in the Italian Renaissance and hailed as
characterizing Western civilization.
Thefirst monument of Islam, the Dome of the Rock (691) took a
rotundal form reminiscent of both a Christianmartyriumand an Arab
memorial structure. It was revetted with gold-and-glass mosaic, a medium
inherited from elite Roman and Sasanian forms coupled with innovatively
monumental architectural Quranic inscriptions.^22 Like the Rotunda at the
Church of the Holy Sepulcher (c.335), the proportions of the Dome of the
Rock conformed to the golden ratio.^23 The proportional similarities of
these buildings, spatially close but temporally distant, suggest shared
aesthetic foundations.
Associations between mathematics and divinity were expressed in the
tenth century, when al-Maqdisi of Balkh likened the necessity of God as
planner of the universe to the need for an architect for a building. Likewise,
al-Ghazali compared God to the planner, builder, and decorator of the
world.^24 The use of the golden ratio to determine the page size and
the placement of the writing in a ninth-century Quran, one of thefirst to
be clearly designed by a foundation associated with the state, indicates the
practical application of such theory. It suggests that the proportions sym-
bolized Platonic associations with cosmic harmony and the divine.^25
Geometric patterning, far more complex than that used under the
Umayyad dynasty, became widespread around the turn of the eleventh
century, particularly under the Abbasid caliphate, ruling from Baghdad,
and the Great Seljuq dynasty (1037–1194), whose capitals were in central(^21) Smith, 1983 ; Jacobson, 1986. (^22) Khoury, 1993 ; Khazaie, 2005.
(^23) Chen, 1979 ; Chen, 1980. (^24) Necipoğlu, 1995 :4. (^25) George, 2003.
274 Mimetic Geometries