“3D Thinking” Pages 187, 274: Using close-packing circles to create surface designs, during the early years of Islam, requires a method to generate different close-packing circle arrangements. The dynamic sphere geometry provides such a method. Applying the geometry, starting with a 5-circle arrangement within the unit triangle of a square, generates many arrangements including the arrangement (8th in the sequence) that was used to create the window design of the 1356CE Madrasa of Amir Salf al-din Sargatmish in Old Cairo, Egypt. Basically the method requires algorithmic steps where circle sizes and positions are changed in a step-by-step fashion. Once one understands the dynamics of the geometry then looking at the Madrasa window in old Cairo becomes a dynamic experience that couples with the numerology of the window itself, for example, 5, 6 and 7 (سنع; نزخ; نوذ) – a repository, a place of wealth. Connecting circle contact and center points with rosettes and straight lines will create surface designs or lattices of which some will have been used in the past.

Supplement  

 

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