Indian mathematics links trigonometry and astronomy

The Bur-Sagale eclipse was recorded in the Assyrian eponym lists. Its date, 15 June 763 BCE, anchors Near Eastern chronology.

Modern astronomical calculation connects the ancient record to an exact day, helping date rulers and events across Assyrian history.

Long sequences of observations enabled scholars to identify regularities in celestial events and refine numerical schemes.

The record shows that numerical astronomy and chronological calculation flourished in Mesopotamia centuries before classical Greek science.

Aryabhata's parameters are reckoned for mean noon at Ujjain on 21 March 499, giving his mathematical astronomy a precise temporal starting point.

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.