Mathematics at work: water tunnels and ceilings

These records pair mathematics and building knowledge with a job on a building or on water. As you read, list the school subjects involved and the person who would use them.

The TDV encyclopaedia, in the record on the architect, reports an order from Sinan's time that no one should build without the chief architect's knowledge. It followed buildings that fell or burned after being put up by men from Rumeli and elsewhere, who worked "with a yard-stick in hand" without knowing carpentry or masonry ². From the sixteenth century, an architect, a journeyman or a master working outside the office needed a licence from the chief architect attesting his competence ². The architect was expected to know geometry, building technique and the measurement of land ².

The museum's records preserve no sentence in which al-Karaji or al-Kashi says why he took up his work. They show the problem each work answers. Al-Karaji's manual follows water from exploration to maintenance and handover ³, and a later manuscript introduces levels the author says he devised ⁴. For al-Kashi, MacTutor describes the book's intended mathematics for astronomy, surveying, architecture, accounting and commerce ⁵, and Dold-Samplonius connects area with possible estimates of the paint or gilding a building needs ⁶.

These two records are easy to read as inventions of the thing itself. The records say otherwise. The 2020 study places qanats in traditions far older than al-Karaji, and it does not credit him with creating the system ⁷. Al-Kashi's method is a calculation method within an older architectural practice, not an attribution of muqarnas itself to one inventor ⁸.

The record on al-Karaji says a straight tunnel can climb, while one with the intended fall can deviate sideways ⁹. If a crew could measure only one of the two, height or direction, which would you choose, and what would still go wrong without the other?

• The architect: the order that stopped building without the chief architect's knowledge, and what an architect was expected to know.
• Al-Karaji's levelling and tunnel alignment: how height is kept apart from direction underground.
• Al-Kashi's muqarnas mensuration: how a ceiling of many small faces becomes a calculation.
• The muqarnas: the tiered cellular ceiling that al-Kashi measures.