Monday, 18 August 2008

Bits and Bobs

Excerpt from The Golden Ratio, by Mario Livio (2002)

P87: ... with the overall withering of intellectual curiosity in the West, interest in the Golden Ratio entered a long period of hibernation. The great Alexandrian library was destroyed by a series of attacks, first by the Romans and then by Christians and Muslims. Even Plato's Academy came to an end in A.D. 529, when the Byzantine emperor Justinian ordered the closing of all the Greek schools. During the depressing Dark Ages that followed, the French historian and bishop Gregory of Tours (538-594) lamented that "the study of letters is dead in our midst." In fact, the whole enterprise of science was essentially transferred in its entirety to India and the Arab world. A significant event of this period was the introduction of the so-called Hindu-Arabic numerals and of decimal notation...

... With the ascendancy of Islam, the Muslim world became an important center for mathematical study. Had it not been for the intellectual surge in Islam during the eighth century, most of the ancient mathematics would have been lost. In particular, Caliph-al-Mamun (786-833) established in Baghdad the Beit al-hikma (House of wisdom), which operated in a similar fashion to the famous Alexandrian university or "Museum." Indeed, the Abbasid empire subsumed any Alexandrian learning that had survived. According to tradition, after having a dream in which Aristotle appeared, the caliph decided to have all the ancient Greek works translated.

Many of the important Islamic contributions were algebraic in nature and touched on the Golden Ration only very peripherally. Nevertheless, at least three mathematicians should be mentioned: Al-Khwarizmi and Abu Kamil Shuja in the ninth century and Abu'l-Wafa in the tenth century.

Mohammed ibn-Musa al-Khwarizmi composed, in Baghada (at about 825), what is considered to be the most influential algebraic work of the period Kitah al-jabr wa al-muqabalah (The science of restoration and reduction). From this title ("al-jabr") comes the word "algebra" that we use today, since this was the first textbook used in Europe on that subject matter. Furthermore, the word "algorithm," used for any special method for solving a mathematical problem using a collection of exact procedural steps, comes from a distortion of al-Khwarizmi's name..."

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