Free Reading Passage on Advances in Mathematics by Nasir al-Din al-Tusi for Unit 1 of AP World History

Cate O'Donnell

2 min read

Jun 9

Advances in mathematics by Nasir al-Din al-Tusi of Dar al-Islam is an illustrative example for the Developments in Dar al-Islam section of Unit 1 of AP World History. You could reference this example on your AP World History test.

Astronomical Observatory of Nasir al-Dīn Tusi/public domain

During the medieval period, the Islamic world was a vibrant center of scientific knowledge and innovation, particularly in the field of mathematics. Among the luminaries of this era, Nasir al-Din al-Tusi stands out not only for his intellectual contributions but also for his unique historical circumstances, notably his interactions with the Mongols.

Nasir al-Din al-Tusi was born in 1201 in Tus, in what is now Iran. His life took a dramatic turn due to the Mongol invasions of the Islamic world. In 1256, after the Mongols conquered the Ismaili fortress where he was residing, al-Tusi was taken into the service of the Mongol ruler Hulagu Khan, a grandson of Ghengis Khan. This pivotal moment led to the establishment of the Maragha observatory in present-day Iran, an institution that al-Tusi would lead. The observatory became a leading center for astronomical study and attracted scholars from across the Islamic world.

Under Mongol patronage, al-Tusi made his most significant contributions. He wrote extensively on astronomy, ethics, logic, philosophy, and mathematics, influencing not only the Islamic scholars of his time but also later European thinkers. His most famous mathematical invention, the Tusi-couple, described linear motion as the sum of two circular motions and was critical in the development of astronomical models by later scholars, including Copernicus.

Al-Tusi's "Treatise on the Quadrilateral" was a groundbreaking work on spherical trigonometry. It refined and expanded upon earlier understandings of the subject and treated trigonometry as an independent discipline for the first time. This text was instrumental in improving the accuracy of astronomical models. Furthermore, his "Al-Shakl al-Qatta’" or "The Transversal Figure," introduced new problems in geometry and provided innovative solutions that advanced the field significantly.

The support of the Mongols was crucial in allowing al-Tusi the resources and security to conduct his research and writing, illustrating how the Mongol Empire contributed to the intellectual life in the territories under its control. The Maragha observatory, in particular, is a testament to the Mongol's significant, albeit indirect, contribution to scientific progress.

Al-Tusi’s works were translated into Latin and were fundamental to the Renaissance recovery of ancient Greek mathematics and astronomy. His influence extends beyond the Islamic world, underscoring the interconnectedness of medieval scholars across different cultures.