Shah Rokh and his wife, Goharshad, a Turkish princess, were very interested in the sciences, and they encouraged their court to study the various fields in great depth.

Students from all over the Middle East and beyond, flocked to this academy in the capital city of Ulugh Beg's empire.

Al-Kashi was still working on his book, called “Risala al-watar wa’l-jaib” meaning “The Treatise on the Chord and Sine”, when he died, in 1429.

Al-Kashi produced sine tables to four sexagesimal digits (equivalent to eight decimal places) of accuracy for each degree and includes differences for each minute.

[9] He wrote the book Sullam al-sama' on the resolution of difficulties met by predecessors in the determination of distances and sizes of heavenly bodies, such as the Earth, the Moon, the Sun, and the Stars.

The accuracy of al-Kashi's estimate was not surpassed until Ludolph van Ceulen computed 20 decimal places of π 180 years later.

In algebra and numerical analysis, he developed an iterative method for solving cubic equations, which was not discovered in Europe until centuries later.

to find roots of N. In western Europe, a similar method was later described by Henry Briggs in his Trigonometria Britannica, published in 1633.

[18] In order to determine sin 1°, al-Kashi discovered the following formula, often attributed to François Viète in the sixteenth century:[19]

The method used when two sides and their included angle were given was essentially the same method used by 13th century Persian mathematician Naṣīr al-Dīn al-Ṭūsī in his Kitāb al-Shakl al-qattāʴ (Book on the Complete Quadrilateral, c. 1250),[20] but Al-Kashi presented all of the steps instead of leaving details to the reader: Another case is when two sides and the angle between them are known and the rest are unknown.

We take the square root of the sum to get the remaining side....Using modern algebraic notation and conventions this might be written After applying the Pythagorean trigonometric identity

[22][23] In discussing decimal fractions, Struik states that (p. 7):[24] "The introduction of decimal fractions as a common computational practice can be dated back to the Flemish pamphlet De Thiende, published at Leyden in 1585, together with a French translation, La Disme, by the Flemish mathematician Simon Stevin (1548-1620), then settled in the Northern Netherlands.

[26] The properties of binomial coefficients were discussed by the Persian mathematician Jamshid Al-Kāshī in his Key to arithmetic of c.

This knowledge was shared by some of the Renaissance mathematicians, and we see Pascal's triangle on the title page of Peter Apian's German arithmetic of 1527.