ALGORITHMS

By Rafat Damseh,
PhD candidate at Polytechnique School of Montreal

ALGORITHMS! Computer technologies  we exhibit nowadays, with all its computer science theoretical basis, are simply based on algorithms. The origin of the word “algorithm” goes back to the 9th century, being derived from the name of one of the most notable scholars in history, who is given sometimes the title of “grandfather of computer science”.

Muhammad Ibn-Musa Al-Khwarizmi (780-850), a muslim mathematician, astronomer, and geographer who was a scholar in the House of Wisdom in Baghdad, the capital of the Islamic Empire/Caliphate. Baghdad was the centre of scientific studies and trade, and many merchants and scientists from as far as China and India traveled to this city, as did Al-Khwarizmi. He wrote all his works in Arabic, the language of science of his time.

Al-Khwarizmi's work on elementary algebra, “Al-Kitab al-mukhtaṣar fi ḥisab al-jabr wal-muqabala” (The Compendious Book on Calculation by Completion and Balancing), was translated into Latin in the 12th century, from which the title and term Algebra derives. Algebra is a compilation of rules, together with demonstrations, for finding solutions of linear and quadratic equations based on intuitive geometric arguments, rather than the abstract notation now associated with the subject. Its systematic, demonstrative approach distinguishes it from earlier treatments of the subject. It also contains sections on calculating areas and volumes of geometric figures and on the use of algebra to solve inheritance problems according to proportions prescribed by Islamic law. Another work by al-Khwarizmi introduced Hindu-Arabic numerals and their arithmetic to the West. It is preserved only in a Latin translation “Algoritmi de numero Indorum” (Al-Khwarizmi Concerning the Hindu Art of Reckoning). From the name of the author, rendered in Latin as Algoritmi, originated the term algorithm.

In addition to his work in mathematics, Al-Khwarizmi made important contributions to astronomy, also largely based on methods from India, and he developed the first quadrant, an instrument used to determine time by observations of the Sun or stars, the second most widely used astronomical instrument during the Middle Ages after the Astrolabe. He also produced a revised and completed version of Ptolemy's, now noted as Geography, consisting of a list of 2,402 coordinates of cities throughout the known world. He also assisted in the construction of a world map for Al-Mamun, the islamic caliph at that time, and participated in a project to determine the circumference of the Earth, which had long been known to be spherical, by measuring the length of a degree of a meridian through the plain of Sinjar in Iraq. Al-Khwarizmi also compiled a set of astronomical tables, based on a variety of Hindu and Greek sources. This work included a table of sines, evidently for a circle of radius 150 units. Like his treatises on algebra and Hindu-Arabic numerals, this astronomical work (or an Andalusian revision thereof) was translated into Latin.


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