A leading scientist at Ulugh Beg's observatory in Samarkand. He calculated π to sixteen decimal places — a record that stood for about 180 years.
From Kashan to Samarkand
Ghiyath al-Din Jamshid al-Kashi was born around 1380 in Kashan, in Iran, and had made his name as an astronomer and calculator before Ulugh Beg invited him to Samarkand. There he became the leading scientist of the new madrasa and observatory. In letters to his father he describes debates in which the prince himself took part — and his colleagues' mistakes — with unconcealed pride.
Sixteen digits of π
In 1424, in his Treatise on the Circumference, al-Kashi calculated 2π to sixteen decimal places by working out the perimeter of a polygon with 805,306,368 sides. He had decided in advance how accurate the answer needed to be — enough to measure the circumference of the universe to within a hair's breadth — and then did the arithmetic to reach it. No one surpassed the result for about 180 years.
The key to arithmetic
His Key to Arithmetic (1427), written for students, merchants and surveyors, set out calculation with decimal fractions more fully than anyone before him, along with methods for extracting roots. He also designed astronomical instruments, including a device for computing planetary positions. He died in 1429 at the Samarkand observatory, before the star tables he had worked on were finished.
Key achievements
- Calculated π to sixteen decimal places in 1424, a record for about 180 years
- Wrote The Key to Arithmetic (1427), a textbook that set out decimal fractions in full
- Helped plan Ulugh Beg's observatory and designed astronomical instruments