Islamic Scholar: Nasir Al-Din Al-Tusi

23 Jan

   

(1201-1274 C.E.)

Nasir al-Din was one of the greatest scientists, philosaphers, mathematicians, astronomers, theologians and physicians of the time and was a prolific writer. He made significant contributions to a large number of subjects, and it is indeed difficult to present his work in a few words. He wrote one or several treatises on different sciences and subjects including those on geometry, algebra, arithmetic, trigonometry, medicine, metaphysics, logic, ethics and theology. In addition he wrote poetry in Persian.

One of al-Tusi’s most important mathematical contributions was the creation of trigonometry as a mathematical discipline in its own right rather than as just a tool for astronomical applications. In Treatise on the quadrilateral al-Tusi gave the first extant exposition of the whole system of plane and spherical trigonometry. As stated in [1]:-

This work is really the first in history on trigonometry as an independent branch of pure mathematics and the first in which all six cases for a right-angled spherical triangle are set forth.

This work also contains the famous sine formula for plane triangles:

a/sin A = b/sin B = c/sin C.

Another mathematical contribution was al-Tusi’s manuscript, dated 1265, concerning the calculation of n-th roots of an integer; see [6] for details of a copy of this manuscript made in 1413. This work by al-Tusi is almost certainly not original but rather it is his version of methods developed by al-Karaji‘s school. In the manuscript al-Tusi determined the coefficients of the expansion of a binomial to any power giving the binomial formula and the Pascal triangle relations between binomial coefficients.

We should mention briefly other fields in which al-Tusi contributed. He wrote a famous work on minerals which contains an interesting theory of colour based on mixtures of black and white, and included chapters on jewels and perfumes. He also wrote on medicine, but his medical works are among his least important. Much more important were al-Tusi’s contributions to philosophy and ethics. In particular in philosophy he asked important questions on the nature of space.

A <a href="http://reference.findtarget.com/search/Persia/">Persia</a>n (<a href="http://reference.findtarget.com/search/Iran/">Iran</a>ian) astrolabe from 1208 As the chief scientist at the observatory established under his supervision at Maragha, he made significant contributions to astronomy. The observatory was equipped with the best possible instruments, including those collected by the Mongol armies from Baghdad and other Islamic centres. The instruments included astrolabes, representations of constellations, epicycles, shapes of spheres, etc. He himself invented an instrument ‘turquet’ that contained two planes. After the devoted work of 12 years at the observatory and with the assistance of his group, he produced new astronomical tables called Al-Zij-Ilkhani dedicated to Ilkhan (Halagu Khan). Although Tusi had contemplated completing the tables in 30 years, the time required for the completion of planetary cycles, but he had to complete them in 12 years on orders from Halagu Khan. The tables were largely based on original observa- tions, but also drew upon the then existing knowledge on the subject. The Zij Ilkhani became the most popular tables among astronomers and remained so till the 15th century. Nasir al-Din pointed out several serious shortcomings in Ptolemy’s astronomy and foreshadowed the later dissatisfaction with the system that culminated in the Copernican reforms.

Tusi’s influence has been significant in the development of science, notably in mathematics and astronomy. His books were widely consulted for centuries and he has been held in high repute for his rich contributions.

Sources: ummah.com & history

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