algorithm

Submitted by b soetoro (Indonesia), Jul 20, 2010 at 21:58

some story about algorithm:

Muhamad ibn Musa
Al-Khowarizmi

(780 - 850)

He wrote several books on astronomy, one on algebra and another one on arithmetics (translated into Latin in the IXth century) in which he makes a complete exposition of the hindi system of numbers. At the beginning, the system was known as "Al Juarizmi's " and because of a malformation, the translation was "Algorithm". Nowadays, the word "Algorithm" means a series of operative procedures which allow to solve any problems of a determined class. No doubt it's due to Al Khowarizmi the origin of this word.

During the first century of the Muslim Empire, there was no scientific development, since the Arabs had not been able to set the necessary intellectual impulse. It was from the second part of the eighth century when the crazy process of translating all the known Greek works into the Arab began.

All over the Empire, schools were founded. On top of them was Bait Al-Hikma (Home of Knowledge). Among the members of this school stands out the name of Mohammed ibn-Musa Al-Khowarizmi who wrote more than half a dozen of Maths and Astronomy books, two of which have had special importance in history. The first of them is based on an Arab translation of Brahmagupta and in it there is an exact reproduction of the Hindi system of numbers, which has originated the popular belief that our system of numbers comes from the Arab. The new system of numbers was known as "Al-Khowarizmi's", then "algorismi" and eventually as algorithm. The same process happened with the word "algebra" which comes from the title of one of his most important books, Hisab al-jabr wa-al-muqabala. In this work six types of cuadratic equations are studied, as well as an outstanding number of Greek elements.

After Al-Khuwarizmi, a great deal of procedures of calculus and special algorithms were developed, among them:

• obtention of number pi with 17 exact figures by means of polygons inscribed and circumscribed in the circumference made by Kashi (s. XV).
• Calculus of roots by the method nowadays known as Ruffini-Horner, possibly as the result of the collaboration with the Chinese Mathematicians.
• Apprioximate extraction of roots, using the lineal interpolation.
• Addition of arithmetic and geometric progressions.

The Arab algebraic works between the IXth and XVth centuries, apart from the resolution of equations of the first and second order, included the cubic equations. To these equations led different kinds of problems, such as the division of a sphere by a plane, the trisection of the angle, the search of the side of a regular polygon of 9 sides and so on.

Apart form the separation from the algebra, the most important characteristic of the Arab mathematics was the formation of the trigonometry. In relation to the problems of astronomy, they made charts of the trigonometric functions with a great frequency and a high degree of accuracy, not only in plane but also in spheric trigonometry.

Al Khowarizmi was a great mathematician and astronomist and a member of "The House of Knowledge", founded in Bagdad (809-833), in which wise men, jews and christians coming from Syria, Iran and Mesopotamia, worked together.

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