The Round City's design expresses applied geometry

His verse describes a rule yielding 3.1416, demonstrating sophisticated numerical work expressed through Sanskrit mnemonic poetry.

Aryabhata's notation encoded numbers through syllables, showing that mathematical representation can take forms other than modern written numerals.

The new Abbasid capital was founded on 30 July 762 and became a major center for scholarship, administration and translation.

Naubakht and Masha'allah reportedly selected an astrologically auspicious moment, illustrating the close relationship between mathematical astronomy and state planning.

The city's multilingual scholarly environment later supported translations and original work in arithmetic, algebra, geometry and astronomy.

Al-Azhar opened in Fatimid Cairo and developed into a long-lived institution of learning.

Alongside religious and linguistic studies, scholars taught inheritance arithmetic, astronomy, timekeeping and related mathematical subjects.

Al-Azhar shows how mathematics was transmitted through teaching communities rather than only through famous books and individuals.

Students from Africa, Asia and the wider Islamic world carried methods and texts across linguistic and political boundaries.

The Abbasid caliph surrendered on 10 February 1258, followed by the sack of a city central to centuries of scientific exchange.