Person: Al-Tusi (2), Nasir al-Din
Nasir al-Tusi was an Islamic astronomer and mathematician who joined the Mongols who conquered Baghdad. He made important contributions to astronomy and wrote many commentaries on Greek texts.
Mathematical Profile (Excerpt):
- Al-Tusi was known by a number of different names during his lifetime such as Muhaqqiq-i Tusi, Khwaja-yi Tusi and Khwaja Nasir.
- Al-Tusi was born in Tus, which lies close to Meshed in northeastern Iran high up in the valley of the Kashaf River.
- This was a period in which there would be little peace and tranquillity for great scholars to pursue their works, and al-Tusi was inevitably drawn into the conflict engulfing his country.
- The Twelfth Imam was the main sect of Shi'ite Muslims and the school where al-Tusi was educated was mainly a religious establishment.
- In 1214, when al-Tusi was 13 years old, Genghis Khan, who was the leader of the Mongols, turned away from his conquests in China and began his rapid advance towards the west.
- It would not be too long before al-Tusi would see the effects of these conquests on his own regions, but before that happened he was able to study more advanced topics.
- From Tus, al-Tusi went to Nishapur which is 75 km west of Tus.
- Nishapur was a good choice for al-Tusi to complete his education since it was an important centre of learning.
- There al-Tusi studied philosophy, medicine and mathematics.
- In particular he was taught mathematics by Kamal al-Din ibn Yunus, who himself had been a pupil of Sharaf al-Din al-Tusi.
- While in Nishapur al-Tusi began to acquire a reputation as an outstanding scholar and became well known throughout the area.
- There was, amid the frequent fighting in the region, peaceful havens which attracted al-Tusi.
- When invited by the Isma'ili ruler Nasir ad-Din 'Abd ar-Rahim to join the service of the Assassins, al-Tusi accepted and became a highly regarded member of the Isma'ili Court.
- However, al-Tusi did some of his best work while moving round the different strongholds, and during this period he wrote important works on logic, philosophy, mathematics and astronomy.
- The first of these works, Akhlaq-i nasiri, was written in 1232.
- It was a work on ethics which al-Tusi dedicated to the Isma'ili ruler Nasir ad-Din 'Abd ar-Rahim.
- In 1256 al-Tusi was in the castle of Alamut when it was attacked by the forces of the Mongol leader Hulegu, a grandson of Genghis Khan, who was at that time set on extending Mongol power in Islamic areas.
- Some claim that al-Tusi betrayed the defences of Alamut to the invading Mongols.
- Certainly Hulegu's forces destroyed Alamut and, Hulegu himself being himself interested in science, he treated al-Tusi with great respect.
- It may be that indeed al-Tusi felt that he was being held in Alamut against his will, for certainly he seemed enthusiastic in joining the victorious Mongols who appointed him as their scientific advisor.
- Certainly al-Tusi had made the right move as far as his own safety was concerned, and he would also profit scientifically by his change of allegiance.
- Hulegu was very pleased with his conquest of Baghdad and also pleased that such an eminent scholar as al-Tusi had joined him.
- So, when al-Tusi presented Hulegu with plans for the construction of a fine Observatory, Hulegu was happy to agree.
- It had various instruments such as a 4 metre wall quadrant made from copper and an azimuth quadrant which was the invention of Al-Tusi himself.
- Al-Tusi also designed other instruments for the Observatory which was far more than a centre for astronomy.
- Al-Tusi put his Observatory to good use, making very accurate tables of planetary movements.
- This was not the only important work which al-Tusi produced in astronomy.
- It is fair to say that al-Tusi made the most significant development of Ptolemy's model of the planetary system up to the development of the heliocentric model in the time of Copernicus.
- The aim of al-Tusi with this result was to remove all parts of Ptolemy's system that were not based on the principle of uniform circular motion.
- Among numerous other contributions to astronomy, al-Tusi calculated the value of 51' for the precession of the equinoxes.
- In logic al-Tusi followed the teachings of ibn Sina.
- Al-Tusi wrote many commentaries on Greek texts.
- In the latter work al-Tusi discussed objections raised by earlier mathematicians to comparing lengths of straight lines and of curved lines.
- Al-Tusi argues that comparisons are legitimate, despite the objections that, being different entities, they are incomparable.
- As in the Zij-i Ilkhahi al-Tusi gave tables of sines with entries calculated to three sexagesimal places for each half degree of the argument.
- 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.
- 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.
- Much more important were al-Tusi's contributions to philosophy and ethics.
- Al-Tusi had a number of pupils, one of the better known being Nizam al-a'Raj who also wrote a commentary on the Almagest Ⓣ(The major thesis: from the Arabic 'al-majisti' -- the Arabic translation of the Greek 'Mathematike Syntaxis' later translated into Latin as 'Magna Syntaxis').
Born 18 February 1201, Tus, Khorasan (now Iran). Died 26 June 1274, Kadhimain (near Baghdad now in Iraq).
View full biography at MacTutor
Tags relevant for this person:
Ancient Arab, Astronomy, Origin Iran
Thank you to the contributors under CC BY-SA 4.0! 
- Github:
-
- non-Github:
- @J-J-O'Connor
- @E-F-Robertson
References
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive
