Islamic architectural geometry left almost no treatises explaining itself, and for a long time that silence was filled with speculation. What it left instead were working documents, and the most important survivor is the Topkapi Scroll, a long roll of pattern drawings from the Timurid-Turkmen world of the fifteenth or sixteenth century, now in the Topkapi Palace Library in Istanbul.
The art historian Gulru Necipoglu, who published the scroll in full, showed what kind of document it is: not a book of doctrine but a designer's repertory, pattern after pattern drawn with the construction lines left visible. Under the inked strapwork run faint uninked lines, scored with a stylus, recording the polygonal scaffolding on which each knot was built. A workshop that owned such a scroll owned the grammar of girih: an apprentice could lift the construction, scale it to a wall or a dome, and adapt it to brick, stucco, wood or tile. Necipoglu drew a further conclusion from the working papers. The geometry was a craft literacy shared between architects, mathematicians and artisans, taught by demonstration and transmitted in scrolls like this one, rather than an esoteric symbolism handed down beside the patterns. Where meaning was attached to the work, it was attached by writers and patrons in particular times and places, not carried inside the knots themselves. The scroll, in other words, answers the how of girih precisely, and leaves the why to history.