Al-Khwarizmi: The Father of Algebra

Bidang Sains

Abu Ja’far Muhammad ibn Musa al-Khwarizmi, (780 – 850 CE), was the grandfather of computer science and the father of Algebra.
He was the popularizer of Arabic numerals, adopter of zero (the symbol) and the decimal system, astronomer, cartographer, in brief an encyclopedic scholar.

Bayt Al-Hikmah (House of Wisdom)

In the year 832, the Abbasid Caliph Al Ma’mun (b. Baghdad, 786, d. Tarsus, Cilicia, August 833) founded the “House of Wisdom” in Baghdad, a center for study and research similar to the earlier Museum in Alexandria. Its most famous scholars were the mathematicians Muhammad ibn Musa Al-Khwarizmi and the Banu Musa (“sons of Moses”), three brothers who directed the translation of Greek works from Antiquity.
The modern word algorithm is derived from the name, al-Khwarizmi, the best mathematician of his age, thanks to his book, “al-Kitab al-mukhtasar fi Hisab al-jabr w’al-muqabala”, (a book showing how to solve equations and problems derived from ordinary life) which means “The Compendious Book on Calculation by Completion and Balancing”, which later evolved into algebra, was the first written text on the subject. In al-Khwarizmi’s time, algebra was a practical system for solving all kinds of problems “in cases of inheritance, contracts, surveying, tax collection, legacies, partition, lawsuits, and trade, and in all their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computations, and other objects of various sorts and kinds are concerned.” Al-jabr was about removing the negative terms from an equation, while al-muqabala meant “balancing” the values of an equation across an equal sign.
It is the title of this text that gives us the word “algebra”. It is the first book to be written on algebra. In al-Khwarizmi’s own words, the purpose of the book was to teach what was easiest and most useful in arithmetic, such as what was constantly required in cases of inheritance, legacies, partition, lawsuits, and trade, and in all their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computations, and other objects of various sorts and kinds were concerned.
This does not sound like the contents of an algebra text, and indeed only the first part of the book is a discussion of what we would today recognize as algebra. However it is important to realize that the book was intended to be highly practical, and that algebra was introduced to solve real life problems that were part of everyday life in the Islamic empire at that time.

After introducing the natural numbers, al Khwarizmi discusses the solution of equations. Al Khwarizmi's equations are linear or quadratic and are composed of units (numbers), roots (x) and squares (x2). He first reduces an equation to one of 6 standard forms, using the operations of addition and subtraction, and then shows how to solve these standard types of equations. He uses both algebraic methods of solution and the geometric method of completing the square.

The next part of al-Khwarizmi’s Algebra consists of applications and worked examples. He then goes on to look at rules for finding the area of figures such as the circle, and also finding the volume of solids such as the sphere, cone, and pyramid.

The text book of Algebra was intended to be highly practical and it was introduced to solve real life problems that were part of everyday life in the Islamic world at that time. Early in the book al-Khwarizmi wrote:

“When I consider what people generally want in calculating, I fou

nd that it always is a number. I also observed that every number is composed of units, and that any number may be divided into units. Moreover, I found that every number which may be expressed from one to ten, surpasses the preceding by one unit: afterwards the ten is doubled or tripled just as before the units were: thus arise twenty, thirty, etc. until a hundred: then the hundred is doubled and tripled in the same manner as the units and the tens, up to a thousand;… so forth to the utmost limit of numeration.”

Al-Khwarizmi also wrote a treatise on Hindu-Arabic numerals. The Arabic text is lost but a Latin translation, “Algoritmi de numero Indorum” in English “Al-Khwarizmi on the Hindu Art of Reckoning” gave rise to the word algorithm deriving from his name in the title as mentioned earlier. Unfortunately the Latin translation (translated into English) is known to be much changed from al-Khwarizmi’s original text (of which even the title is unknown). The work describes the Hindu place-value system of numerals based on 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. The first use of zero as a place holder in positional base notation was probably due to al-Khwarizmi in this work. Methods for arithmetical calculation are given, and a method to find square roots is known to have been in the Arabic original although it is missing from the Latin version.“… The decimal place-value system was a fairly recent arrival from India and … al-Khwarizmi’s work was the first to expound it systematically. Thus, although elementary, it was of seminal importance.” Khwarizmi developed detailed trigonometric tables containing the sine functions which later included tangent functions. Khwarizmi’s book on arithmetic was translated into Latin and published in Rome in 1857 by Prince Baldassare Boncompagni and appears as part 1 of a volume entitled “Tratti d’ aritmetica”. The book is titled as Algorithmi de numero indorum which means “Khwarizmi concerning the Hindu art of reckoning.” Many of his books were translated into Latin and used as a principle mathematical text book in European universities until the 16th. century. Among them these two books had important place: “Kitab al-Jama wal-Tafreeq bil Hisab al-Hindi” and “Kitab al-Jabr wa al-muqabala.”

Khwarizmi’s contribution and influence are tremendous. Two important books on arithmetic, Carmen de Algorismo and Algorismus vulgaris which were written in 12th. and 13th. century respectively owe a lot to the Khwarizmi’s book and were used for several hundred years in Europe. Abu Kamil Shuja, an Islamic mathematician, whose work on mathematics was based on Khwarizmi’s works kept the influence of Khwarizmi on Leonardo of Pisa, a 13th. century scholar and up to Middle Ages and during the Renaissance.

Astronomy

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Al Khwarizmi also wrote an important work on astronomy, covering calendars, calculating true positions of the sun, moon and planets, tables of sinus and tangents, spherical astronomy, astrological tables, parallax and eclipse calculations, and visibility of the moon. Although his astronomical work is based on that of the Indians, and most of the values from which he constructed his tables came from Hindu astronomers, al-Khwarizmi must have been influenced by Ptolemy’s work too. Al-Khwarizmi performed detailed calculations of the positions of the sun, moon, and planets, and did a number of eclipse calculations. In addition to an important treatise on astronomy, Al-Khwarizmi wrote a book on astronomical tables, which were also translated into European languages and, later, into Chinese.

Geography
In geography, Al Khwarizmi wrote the book called Kitab Surat al- ard (Book of the Form of the Earth). His works differed from Ptolemy’s and he corrected Ptolemy’s views in detail. It is a description of a world (known world at that time) map and contains a list of the coordinates of the important places on it. He corrected the distortion that Ptolemy’s map had with regard to the length of the Mediterranean. It was much more accurate. However, it failed to replace the Ptolemaic geography used in Europe. He wrote many other books on topics such as clocks, sundials and astrolabes.

Al-Khwarizmi wrote a major work on geography which gives latitudes and longitudes for 2,402 cities and landmarks, forming the basis for a world map. The book, which is based on Ptolemy’s Geography, lists with latitudes and longitudes, cities, mountains, seas, islands, geographical regions, and rivers. The manuscript includes maps which on the whole are more accurate than those of Ptolemy.
A number of minor works were written by al-Khwarizmi on topics such as the astrolabe, on which he wrote two works, on the sundial, and on the Jewish calendar. He also wrote a political history containing horoscopes of prominent persons.

Al-Khwarizmi systematized and corrected Ptolemy’s research in geography and astronomy/astrology, using his own original findings. He supervised the work of 70 geographers to create a map of the then “known world”. He is also reported to have collaborated in the degree measurements ordered by Caliph Ma'mun al-Rashid. These were aimed at measuring the volume and circumference of the earth.





.http://www.onislam.net/english/reading-islam/research-studies/islamic-history/454243-al-khwarizmi-the-father-

     Nama sebenar al-Khawarizmi ialah Muhammad Ibn Musa al-khawarizmi. Selain itu beliau dikenali sebagai Abu Abdullah Muhammad bin Ahmad bin Yusoff.  Al-Khawarizmi telah dikanali di Barat sebagai al-Khawarizmi, al-Cowarizmi, al-Ahawizmi, al-Karismi, al-Goritmi, al-Gorismi dan beberapa cara ejaan lagi.

            Beliau telah dilahirkan di Bukhara.  Pada tahun 780-850M adalah zaman kegemilangan al-Khawarizmi.  al-Khawarizmi telah wafat antara tahun 220 dan 230M. Ada yang mengatakan al-Khawarizmi hidup sekitar awal pertengahan abad ke-9M. Sumber lain menegaskan beliau di Khawarism, Usbekistan pada tahun 194H/780M dan meninggal tahun 266H/850M di Baghdad.

Ketokohan al-Khawarizmi

Setiap tokoh mempunyai sifat ketokohannya yang tersendiri.  Ketokohan al-Khawarizmi dapat dilihat dari dua sudut iaitu dari bidang matematik dan astronomi.  Namun bidang matematik akan diperjelaskan secara terperinci berbanding astronomi kerana ia melibatkan kajian yang dikaji.

            Dalam bidang matematik, al-Khawarizmi telah memperkenalkan aljabar dan hisab.  Beliau banyak menghasilkan karya-karya yang masyhor ketika zaman tamadun Islam.  Antara karya-karya yang  beliau hasilkan ialah ‘Mafatih al-Ulum’.  Sistem nombor adalah salah satu sumbangan dan telah digunakan pada zaman tamadun Islam.

            Banyak kaedah yang diperkenalkan dalam setiap karya yang dihasilkan. Antaranya ialah kos, sin dan tan dalam trigonometri penyelesaian persamaan, teorem segitiga sama juga segitiga sama kaki dan mengira luas segitiga, segi empat selari dan bulatan dalam geometri.  Masaalah pecahan dan sifat nombor perdana dan teori nombor juga diperkenalkan.  Banyak lagi konsep dalam matematik yang telah diperkenalkan al-khawarizmi sendiri.

            Bidang astronomi juga membuatkan al-Khawarizmi dikenali pada zaman tamadun Islam.  Astronomi dapat ditakrifkan sebagai ilmu falaq [pengetahuan tentang bintang-bintang yang melibatkan kajian tentang kedudukan, pergerakan, dan pemikiran serta tafsiran yang berkaitan dengan bintang].

            Seawal kurun ketiga lagi lagi, al-Khawarizmi telah menghasilkan dua buah yang salah satu daripadanyatelah diterjemahkan ke Bahasa Latin dan memberi pengaruh besar ke atas Muslim dan orangSpanyol dan Kristian.

            Penggunaan matematik dalam astronomi sebelum tamadun Islam amat sedikit dan terhad.  Ini disebabkan oleh kemunduran pengetahuan matematik yang terhad kepada pengguna aritmetik dan geometri sahaja.