Abū Bakr Muḥammad ibn al Ḥasan al-Karajī (Persian: ابو بکر محمد بن الحسن الکرجی; c. 953 – c. 1029) was a 10th-century Persian mathematician and engineer...

(Paris, 1853), praised Al-Karaji for being "the first who introduced the theory of algebraic calculus". Stemming from this, Al-Karaji investigated binomial...

influencing mathematical thought for an extended period. Successors like Al-Karaji expanded on his work, contributing to advancements in various mathematical...

Abu Ahmad Muhammad bin Ali bin Muhammad al-Karaji, better known as al-Qassab, was a Muslim warrior-scholar, exegete and specialist in Hadith studies....

based on his ability to extract roots. One of Khayyam's predecessors, al-Karaji, had already discovered the triangular arrangement of the coefficients...

by al-Karaji and continued by al-Samaw'al and others was that of an inductive argument for dealing with certain arithmetic sequences. Thus al-Karaji used...

binomial coefficients appears in a work by Al-Karaji, quoted by Al-Samaw'al in his "al-Bahir". Al-Karaji described the triangular pattern of the binomial...

Abū Sahl al-Qūhī Abu-Mahmud al-Khujandi Abū al-Wafā' al-Būzjānī Ibn Sahl Al-Sijzi Ibn Yunus Abu Nasr Mansur Kushyar ibn Labban Al-Karaji Ibn al-Haytham...

Adequate (Kitāb al-kifāya), and Book of the Kernel (Kitāb al-ʿasīr). The works of Abu Kamil influenced other mathematicians, like al-Karaji and Fibonacci...

coefficient can be found in a work by Al-Karaji, quoted by Al-Samaw'al in his "al-Bahir". Cauchy-Riemann Integral: Ibn al-Haytham gave a simple form of this...

Mansur, Abu al-Wafa' al-Buzjani, Ahmad ibn Fadlan, Ali Ibn Isa, Al-Karaji (al-Karkhi), Ibn al-Haytham (Book of Optics), Avicenna, Averroes, and Al-Biruni....

later mathematicians, such as al-Karaji and Fibonacci. Further developments in algebra were made by Al-Karaji in his treatise al-Fakhri, where he extends the...

O'Connor, John J.; Robertson, Edmund F., "Abu Bekr ibn Muhammad ibn al-Husayn Al-Karaji", MacTutor History of Mathematics Archive, University of St Andrews...

Pascal's triangle previously given by al-Karaji. Arabic Wikisource has original text related to this article: al-Samaw'al He also wrote a famous polemic...

b)(c\pm d)} , and al-Karaji wrote in his al-Fakhrī that "negative quantities must be counted as terms". In the 10th century, Abū al-Wafā' al-Būzjānī considered...

used used alum to clarify water as early as 1500 BC. Persian engineer Al-Karaji (c. 953 – c. 1029) wrote a book, The Extraction of Hidden Waters, which...

archbishop of Canterbury (d. 1012) Al-Karaji, Persian mathematician Bermudo II, king of León and Galicia March 19 – al-Mansur bi-Nasr Allah, Fatimid caliph...

al Ḥusayn Al-Karaji (c. 953–1029) wrote on the binomial theorem and Pascal's triangle. In a now lost work known only from subsequent quotation by al-Samaw'al...

and in those of Al-Karaji c. 1000 in Persia. Bressoud (2004) mentions several additional early mathematical works on this formula, by Al-Qabisi (10th century...

to its standard use throughout the region and the world. 953 – Persia, Al-Karaji is the "first person to completely free algebra from geometrical operations...

treatise al-Fakhri (by al-Karajī, 953 – ca. 1029) builds on it to some extent. According to Rashed Roshdi, Al-Karajī's contemporary Ibn al-Haytham knew...

of geomorphology and natural climate change. 1000: Al-Karaji uses mathematical induction. 1058: al-Zarqālī in Islamic Spain discovers the apsidal precession...

phrase were written by Al-Karaji a.k.a. Al-Karkhi (died circa 1029), Umar al-Khayyam (died 1123), and Ibn al-Banna (died 1321). Al-Khwarizmi's algebraic...

Ameli (b. 1961), a scholar of communication Abū Bakr Muḥammad ibn al Ḥasan al-Karajī (Persian: ابو بکر محمد بن الحسن الکرجی; c. 953 – c. 1029) was a 10th-century...

Lorraine) Abu'l-Qasim Jafar, Buyid statesman and vizier (Fasanjas family) Al-Karaji, Persian mathematician and engineer (approximate date) Fujiwara no Kinsue...

inductive proof for arithmetic sequences was introduced in the Al-Fakhri (1000) by Al-Karaji, who used it to prove the binomial theorem and properties of...

triangle was known well before Pascal's time. The Persian mathematician Al-Karaji (953–1029) wrote a now-lost book which contained the first formulation...

the equation for (a, c) equal to (1, 1), (1, −1), (1, 12), and (3, 9). Al-Karaji, a 10th-century Persian mathematician, worked on similar problems to Diophantus...

made various contributions to its solution. These include Aryabhata, Al-Karaji, Ibn al-Haytham, Thomas Harriot, Johann Faulhaber, Pierre de Fermat and Blaise...

mathematician al-Karaji dedicated two of his works to him. His son, Abu Shuja Muhammad al-Ashraf, was briefly vizier of the Fatimid caliph al-Mustansir Billah...