arithmetic, optics, astronomy, weights, and mechanics. Each field
comprised a theoretical and an applied branch.^32
Surviving pattern books reflecting the early development of polyhedral
isometric geometry demonstrate the sophistication with which craftsmen
learned to execute designs that would become commonplace on the surfaces
of objects and architecture. One anonymous Persian-language manuscript
dated between the eleventh and thirteenth centuries and entitled “On
Interlocking Similar or Congruent Figures”exemplifies how basic geome-
trical knowledge created systemic pattern.^33 Recognizing the unprecedented
sophistication of the work, Necipoğlu describes it not as a unique work of
genius so much as a collaborative reflection of the a multi-directional actor
network disseminated widely by artisans, copyists, and scholars.^34
Illustrations include: a demonstration of how to use a sextant in relation to
the stars to determine theqibla[Figure 24]; an association of geometry with
pragmatic knowledge of building construction and astronomy; geometric
exposition of the golden section [Figure 25]; and examples of how to build
repeating patterns with a tripartite ruler and a compass, indicated at the top
ofFigure 26. This also at the bottom ofFigure 27, where a compass has been
used to designate two points outside of the circle. Repetition of this mea-
surement through repositioning the compass and the ruler, or through
repositioning of such diagrams, enables the potentially infinite reproduction
of geometric focal points.
The correlation of geometric surface treatment with the incorporation of
late antique philosophies into Islamic thought reflects contemporaneous
theological debates in Abbasid Baghdad and Fatimid Cairo. The accep-
tance of the Aristotelian idea, expressed in theTopics, that the world could
be rationally understood through principles of knowledge derived from
observation provided a strong substrate for the incorporation of antique
philosophy into Islamic thought in ninth-century Baghdad. Yet for many,
this emphasis on the power of human rational thought implied sacrilegious
limitation of divine omnipotence. Far from a simple transfer of antique
knowledge into Islamic culture through science, these discourses under-
scored the pragmatic engagement of theology with science. The relation-
ship between proportions and aesthetics is handled explicitly in the
Brethren of Purity’s sixth epistle, concerning ratios–first mathematical,
then also in relation to music, alphabetical letters, verse, dyes, medicines,(^32) Necipoğlu,2017a: 20; Kheirandish, 2017 :81–83.
(^33) “Fi Tadakhul al-Ashkal al-Mutashabiha aw al-Mutawafika,”Bibliothèque Nationale de France,
Paris, MS Persan 169; Necipoğlu, 1995 : 146–150; Necipoğlu,2017a.
(^34) Necipoğlu,2017a:57–58.
278 Mimetic Geometries