Friday, November 13, 2009

The Origins of Algebra - al khorezmi

Al khorezmi

The first treatise on algebra was written by Diophantus of Alexandria in the third century AD. The term derives from the Arabic al-jabr or literally "the reunion of broken parts.'' As well as its mathematical meaning, the word also means the surgical treatment of fractures. 'the setting of broken bones'.  Algebra gained widespread use through the title of a book " ilm al-jabr wa'l-mukabala - the science of restoring what is missing and equating like with like".

Written by the mathematician Abu Ja'far Muhammad (active c.800-847), who subsequently has become know as al-Khwarazmi, the man of Khwārazm. The words Algorism (the Arabic or decimal system of writing numbers) and algorithm also both derive from his name.

Abu Jofar Mohammed ben Musa al Khorezmiy al Majusi al-Katrabbuli (Muhammad ibn Musa al-Khwarizmi) was born in 783 in Kath located on the outskirts of Beruni in Southern Karakalpakstan.

In 809, he left for Merv to become a scholar at the court of Al-Mamun, the ruler of the Eastern province of the Caliphate and a famous patron of the arts and sciences. On Al-Mamum assuption of the Caliphate in 819 he followed his patron to Bagdad where he was nominated him head of the House of Wisdom, the first and largest scientific center of the Middle Ages, later called the "Academy of Al-Mamun".

Here from 829 Mohammed Al-Khorezmi wrote more than twenty research works, the most famous of which is the "Concise Book of Calculus in Algebra and Almukabula". It was translated into Latin in the twelfth century; its Arabic and Latin variants have been preserved. Al-Khorezmiy wrote "A Book of Indian Calculus", a work known in the Latin version translated by Adelard Bat in the 12th century; he also wrote the Zij - renowned astronomical tables. The tables were translated into Latin, and those Latin manuscripts remain preserved. Al-Khorezmiy also wrote "The Book of Survey of the Orient" represented by the one and only Arabic manuscript in Strasbourg, France. The manuscript was re-copied in 1037. Fragments of his "Book of history" in Arabic still exist.
Al Khawarizmi was the founder of several basic principles of mathematics. In his "Book of Indian Calculus" he for the first time in science, describes the arithmetical operations of decimal positioning, based on nine digits and zero. His publication spread the concept of zero across the world. He was also the first to describe the concept, written in Latin language of the "algorithm" which signifies "a constant calculating process". Algorithm is one of the basic concepts not only of mathematics, but also cybernetics.

In another book Al-Jabr wa-al-Muqabilah (Book of Calculations, restoration and reduction) is where the word algebra (Al Jabr in Arabic) was first used. Al-Khorezmi was also the first scientist to define and represent algebra as a science. In his work he submitted six canonical types of linear and square equations and basic methods of solving them, methods which are still used.

The word "algebra" was latinised from the Arabic word "al-jabr", which is evident from the Arabic title of the treatise. The word stands for "filling in" - one of the fundamental operations in algebra at that time.

These works tremendously influenced the development of Science in both the Muslim World and in Europe making him one of the most important mathematician, astronomer and geographer of his age.

Source: Wikipedia and


  1. Al-Khwarizmi and quadratic equations.

    The treatise Hisab al-jabr w'al-muqabala was the most famous and important of all of al-Khwarizmi's works. In this book, al-Khwarizmi gives a complete solution to all possible types of quadratic equation.

    Here is an example to al-Khwarizmi's solution of the equation:

    x2 + 21 = 10x.

    In this case the quadratic has two solutions.

    He commented " Halve the number of the roots. It is 5. Multiply this by itself and the product is 25. Subtract from this the 21 added to the square term and the remainder is 4. Extract its square root, 2, and subtract this from half the number of roots, 5. There remains 3. This is the root you wanted, whose square is 9.

    Alternatively, you may add the square root to half the number of roots and the sum is 7. This is then the root you wanted and the square is 49. When you meet an instance which refers you to this case, try its solution by addition, and if that does not work subtraction will. In this case, both addition and subtraction can be used, which will not serve in any other of the three cases where the number of roots is to be halved.

    Know also that when, in a problem leading to this case, you have multiplied half the number of roots by itself, if the product is less than the number of dirhams added to the square term, then the case is impossible. On the other hand, if the product is equal to the dirhams themselves, then the root is half the number of roots".

  2. In the Fibonacci sequence, every number after 0 and 1 is the sum of the previous two numbers, so that the sequence runs: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10,946 and so on. The series appears in nature in many forms, including the spiral arrangements of sunflower seeds, pineapple fruitlets and pinecone scales; it appears in geometry, where, starting with the number 5, every other Fibonacci number is the length of the hypotenuse of a Pythagorean right triangle with integral sides; it recurs in mathematics, where the ratio between successive Fibonacci numbers approaches the classical “golden ratio” of 1:1.618033….

    Like the Polish astronomer Copernicus and the Spanish physician Michael Servetus in the 16th century, Fibonacci, who was one of the founders of western mathematics, constructed a substantial portion of his pioneering scientific research on the foundations laid by his Arabic-speaking predecessors. Using Latin translations of Muhammad ibn Musa al-Khwarizmi’s treatises on algebra and algorithms, Fibonacci, also known as Leonard of Pisa, wrote the Liber abaci, the first widely available book on Arabic numerals and arithmetical problems, expanding Indian-based concepts that had arrived in Spain starting in the 10th century.