Islamic mathematics in the context of "Islamic world contributions to Medieval Europe"

Abū Muḥammad Jābir ibn Aflaḥ (Arabic: أبو محمد جابر بن أفلح, Latin: Geber/Gebir; 1100–1150) was an Arab Muslim astronomer and mathematician from Seville, who was active in 12th century al-Andalus. His work Iṣlāḥ al-Majisṭi (Correction of the Almagest) influenced Islamic, Jewish, and Christian astronomers.

Mīrzā Muhammad Tarāghāy bin Shāhrukh (Chagatay: میرزا محمد تراغای بن شاهرخ; Persian: میرزا محمد طارق بن شاهرخ), better known as Ulugh Beg (Persian: الغ‌بیک; 22 March 1394 – 27 October 1449), was a Timurid sultan, as well as an astronomer and mathematician.

Ulugh Beg was notable for his work in astronomy-related mathematics, such as trigonometry and spherical geometry, as well as his general interests in the arts and intellectual activities. It is thought that he spoke five languages: Arabic, Persian, Chaghatai Turkic, Mongolian, and a small amount of Chinese. During his rule (first as a governor, then outright) the Timurid Empire achieved the cultural peak of the Timurid Renaissance through his attention and patronage. Samarkand was captured and given to Ulugh Beg by his father Shah Rukh.

The Tusi couple (also known as Tusi's mechanism) is a mathematical device in which a small circle rotates inside a larger circle twice the diameter of the smaller circle. Rotations of the circles cause a point on the circumference of the smaller circle to oscillate back and forth in linear motion along a diameter of the larger circle. The Tusi couple is a two-cusped hypocycloid.

The couple was first proposed by the 13th-century Persian astronomer and mathematician Nasir al-Din al-Tusi in his 1247 Tahrir al-Majisti (Commentary on the Almagest) as a solution for the latitudinal motion of the inferior planets and later used extensively as a substitute for the equant introduced over a thousand years earlier in Ptolemy's Almagest.

Abu Zayd Ahmed ibn Sahl Balkhi (Persian: ابو زید احمد بن سهل بلخی) was a Persian Muslim polymath: a geographer, mathematician, physician, psychologist and scientist. Born in 850 CE in Shamistiyan, in the province of Balkh, Greater Khorasan, he was a disciple of al-Kindi. He also founded the "Balkhī school" of terrestrial mapping in Baghdad. Al-Balkhi is believed to have been one of the earliest to diagnose that mental illness can have psychological and physiological causes and he was the first to typify four types of emotional disorders: fear and anxiety; anger and aggression; sadness and depression; and obsessions.

Abū Jaʿfar Muḥammad ibn Jarīr ibn Yazīd al-Ṭabarī (Arabic: أَبُو جَعْفَر مُحَمَّد بْن جَرِير بْن يَزِيد ٱلطَّبَرِيّ; 839–923 CE / 224–310 AH), commonly known as al-Ṭabarī (Arabic: ٱلطَّبَرِيّ), was a Sunni Muslim scholar, polymath, historian, exegete, jurist, and theologian from Amol, Tabaristan, present-day Iran. Among the most prominent figures of the Islamic Golden Age, al-Tabari is widely known for his historical works and expertise in Quranic exegesis, and has been described as "an impressively prolific polymath". He authored works on a diverse range of subjects, including world history, poetry, lexicography, grammar, ethics, mathematics, and medicine. Among his most famous and influential works are his Quranic commentary, Tafsir al-Tabari, and historical chronicle, Tarikh al-Tabari.

Al-Tabari followed the Shafi'i school for nearly a decade before he developed his own interpretation of Islamic jurisprudence. His understanding of it was both sophisticated and remarkably fluid, and, as such, he continued to develop his ideas and thoughts on juristic matters right until the end of his life.

Abū Ḥanīfa Aḥmad ibn Dāwūd Dīnawarī (Arabic: أبو حنيفة أحمد بن داود الدينوري; died 895) was an Islamic Golden Age polymath: astronomer, agriculturist, botanist, metallurgist, geographer, mathematician, and historian.

Arab studies or Arabic studies is an academic discipline centered on the study of Arabs and Arab World. It consists of several disciplines such as anthropology, sociology, linguistics, historiography, archaeology, cultural studies, economics, geography, international relations, law, literature, philosophy, psychology, political science, and public administration. The field draws from old Arabic chronicles, records and oral literature, in addition to written accounts and traditions about Arabs from explorers and geographers in the Arab World (Middle East-North Africa).